DANIEL D. ANDERSON
BIRTHDATE/PLACE
12/20/48; Ft. Dodge, Iowa
EDUCATION
BA, University of Iowa, 1971 Phi Beta Kappa, Collegiate Scholar, Woodrow Wilson Fellow
MS, University of Chicago, 1971 NSF Fellow
Ph.D., University of Chicago, 1974 NSF Fellow
PROFESSIONAL EXPERIENCE
Visiting Assistant Professor of Mathematics, University of Iowa, 1974-75
Assistant Professor of Mathematics, Virginia Tech, 1975-76
Assistant Professor of Mathematics, University of Missouri, Columbia, 1976-77
Assistant Professor of Mathematics, University of Iowa, 1977-79
Associate Professor of Mathematics, University of Iowa, 1979-83
Professor of Mathematics, University of Iowa, 1983-
Ph.D. STUDENTS
Joaquin Pascual-Garcia, Prüfer Rings, Strong N-Rings and r-Lattices of Ideals of Commutative Rings, August 1986
Byung Gyun Kang, *-Operations on Integral Domains, August 1987
Richard Spellerberg, Some Problems in Multiplicative Lattice Theory, August 1990
Rebecca Lewin, Generalizations of GCD-domains and Related Topics, May 1991
Kent Knopp, Ideals Generated by Powers of Elements, August 1991
Muhammad Naseer, Colorings of Commutative Rings, May 1992
Jeanam Park, Finitely Generated Monoids of Fractional Ideals and Related Topics, August 1992
Francisco Alarcon, The Lattice of Ideals of a Semiring, August 1992
Silvia Valdes-Leon, Factorization in Commutative Rings with Zero Divisors, August 1993
Bernadette Mullins, Finiteness Theorems for Factorization in Integral Domains, May 1995
Susan LaGrassa, Semirings: Ideals and Polynomials, May 1995
Roy Quintero, Some Generalizations of GCD-domains, May 1997
Joe Stickles, Commutative Rings with Finitely Generated Multiplicative Semigroup, July 1998
Sylvia Cook, Two Star Operations and their Induced Lattices, July 1999
Michael Axtell, U-factorizations in Commutative Rings with Zero Divisors, July 2000
Eric Smith, Weakly Prime Ideals, July 2001
Myung-Sook Ahn, Weakly Clean Rings and Almost Clean Rings, August 2003
Sharon Clarke, Star-Operations Induced by Overrings, August 2003
John Robeson, Irredundant Generating Sets for Modules, August 2003
Mike Winders, Idealization, July 2004
Amit Ganatra, Some Topics in Factorization in Commutative Rings with Zero Divisors, December 2005
Andrea Frazier, Generalized Factorization in Integral Domains, May 2006
Malik Bataineh, Generalizations of Prime Ideals, July 2006
BOOKS
1. Commutative Algebra, Vols. I and II, Lecture Notes by Daniel Anderson, Department of Mathematics, University of Chicago, Chicago, Ill., Vol. I, 1975, iii+119, Vol. II, 1976, ii+119 (P.M. Murthy). (A revision is being published by Tata Institute/AMS)
2. Student Solutions Manual for Stewart's Calculus (Volume I), Brooks/Cole Publishing Company, Monterey, California, 1987 (with D. Drucker), Second edition, 1991, Third edition, 1995, Fourth edition, 1999, Fifth edition, 2003, Sixth edition, 2008.
3. Factorization in Integral Domains (editor), Marcel Dekker, Inc., New York, 1997.
4. Ideal Theoretic Methods in Commutative Algebra: In Honor of James A. Huckaba's Retirement (editor with Ira Papick), Marcel Dekker, New York, 2001.
1. 1991 Iowa Trade Tokens Supplement, 49 pages, published by author.
2. A token from my grandfather’s general store, Talkin’ Tokens 64 (2002), 52-53.
MATHEMATICAL PUBLICATIONS
1. The Krull intersection theorem, Pacific Journal of Mathematics 57 (1975), 11-14.
2. A remark on the lattice of ideals of a Prüfer domain, Pacific Journal of Mathematics 57 (1975), 323-324.
3. Distributive Noether lattices, Michigan Mathematical Journal 22 (1975), 109-115.
4. The existence of dual modules, Proceedings of the American Mathematical Society 55 (1976), 258-260.
5. Multiplication ideals, multiplication rings, and the ring R(X), Canadian Journal of Mathematics 28 (1976), 760-768.
6. The Krull intersection theorem II, Pacific Journal of Mathematics 66 (1976), 15-22 (with J. Matijevic and W. Nichols).
7. Abstract commutative ideal theory without chain condition, Algebra Universalis 6 (1976), 131-145.
8. Arithmetically embeddable local Noether lattices, Michigan Mathematical Journal 23 (1976), 177-184 (with E. W. Johnson).
9. Weak join-principal element lattices, Algebra Universalis 6 (1976), 377-381 (with E. W. Johnson).
10. Fake rings, fake modules, and duality, Journal of Algebra 47 (1977), 425-432.
11. Another generalization of principal ideal rings, Journal of Algebra 48 (1977), 409-416.
12. Artinian modules are countably generated, Colloquium Mathematicum 28 (1977), 5-6.
13. Some remarks on the ring R(X), Commentariorum Mathematicorum Universitatis Sancti Pauli 26 (1977), 137-140.
14. Radical ideals of principal class, Studia Mathematica 12 (1977), 37-39.
15. Multiplicative lattices in which every principal element is a product of prime elements, Algebra Universalis 8 (1978), 330-335.
16. Integral closure in Noetherian rings II, Communications in Algebra 6 (1978), 639-657 (with J. A. Huckaba).
17. p-domains, overrings, and divisorial ideals, Glasgow Mathematical Journal 19 (1978), 199-203.
18. Some finiteness conditions on a commutative ring, Houston Journal of Mathematics 4 (1978), 289-299.
19. Graded p-rings, Canadian Journal of Mathematics 31 (1979), 449-457 (with J. Matijevic).
20. Unique factorization and small regular local Noether lattices, Journal of Algebra 59 (1979), 260-263 (with E. W. Johnson).
21. Noether lattices representable as quotients of the lattice of monomially generated ideals of polynomial rings, Canadian Journal of Mathematics 31 (1979), 789-799 (with E. W. Johnson and J. A. Johnson).
22. Generalized GCD domains, Commentariorum Mathematicorum Universitatis Sancti Pauli 28 (1979), 215-221 (with D. F. Anderson).
23. Global transforms and Noetherian pairs, Hiroshima Mathematical Journal 10 (1980), 69-74.
24. Noetherian rings in which every ideal is a product of primary ideals, Canadian Mathematical Bulletin 23 (1980), 457-459.
25. Some remarks on multiplication ideals, Mathematica Japonica 25 (1980), 463-469.
26. Some ideal-theoretic conditions on a Noetherian ring, Houston Journal of Mathematics 7 (1981), 1-10 (with D. F. Anderson and E. W. Johnson).
27. Noether lattices: some constructions and decompositions, Fundamenta Mathematica 114 (1981), 11-16 (with A. Boals and E. W. Johnson).
28. Divisibility properties of graded domains, Canadian Journal of Mathematics 34 (1982), 196-215 (with D. F. Anderson).
29. Divisorial ideals and invertible ideals in a graded integral domain, Journal of Algebra 76 (1982), 549-569 (with D. F. Anderson).
30. Globalization of some local properties in Krull domains, Proceedings of the American Mathematical Society 85 (1982), 141-145.
31. Grading integral domains, Communications in Algebra 11 (1983), 1-19 (with D. F. Anderson).
32. Structure and embedding theorems for small strong-p-lattices, Algebra Universalis 16 (1983), 147-152 (with E. W. Johnson and J. A. Johnson).
33. On the ideal equation I(BÇC) = IBÇIC, Canadian Mathematical Bulletin 26 (1983), 331-332.
34. Some remarks on cancellation ideals, Mathematica Japonica 29 (1984), 879-886 (with D. F. Anderson).
35. Join-principally generated multiplicative lattices, Algebra Universalis 19 (1984), 74-82 (with E. W. Johnson).
36. Some finiteness and divisibility conditions on the proper overrings of an integral domain, Communications in Algebra 12 (1984), 1689-1706 (with D. F. Anderson, D. E. Dobbs, and
E. G. Houston).
37. Locally factorial integral domains, Journal of Algebra 90 (1984), 265-283 (with D. F. Anderson).
38. Ideal theory in commutative semigroups, Semigroup Forum 30 (1984), 127-158 (with E. W. Johnson).
39. Unique factorization rings with zero divisors, Houston Journal of Mathematics 11 (1985), 15-30 (with R. Markanda).
40. Unique factorization rings with zero divisors. Corrigendum, Houston Journal of Mathematics 11 (1985), 423-426 (with R. Markanda).
41. Finite intersections of PID or factorial overrings, Canadian Mathematical Bulletin 28 (1985), 91-97 (with D. F. Anderson).
42. The rings R(X) and R<X>, Journal of Algebra 95 (1985), 96-115 (with D. F. Anderson and R. Markanda).
43. Generalizations of Boolean rings, Boolean-like rings and von Neumann regular rings, Commentariorum Mathematicorum Universitatis Sancti Pauli 35 (1986), 69-76.
44. A new characterization of Dedekind domains, Glasgow Mathematical Journal 28 (1986), 237-239 (with E. W. Johnson).
45. Multiplicatively closed subsets of fields, Houston Journal of Mathematics 13 (1987), 1-11 (with D. F. Anderson).
46. A note on stable domains, Houston Journal of Mathematics 13 (1987), 13-17 (with J. Huckaba and I. Papick).
47. Locally almost factorial integral domains, Journal of Algebra 105 (1987), 395-410 (with D. F. Anderson).
48. Commutative rings in which every ideal is a product of primary ideals, Journal of Algebra 106 (1987), 528-535 (with L. A. Mahaney).
49. Characterizing Prüfer rings via their regular ideals, Communications in Algebra 15 (1987), 1287-1295 (with J. Pascual).
50. On a result of M. Martin concerning the number of generators of products of invertible ideals, Communications in Algebra 15 (1987), 1765-1768.
51. Regular ideals in commutative rings, sublattices of regular ideals and Prüfer rings, Journal of Algebra 111(1987), 404-426 (with J. Pascual).
52. Nonfinitely generated ideals in valuation domains, Tamkang Journal of Mathematics 18 (1987), 49-52.
53. Flatness, LCM-stability, and related module-theoretic properties, Journal of Algebra 112 (1988), 139-150 (with D. E. Dobbs).
54. Some remarks on star operations and the class group, Journal of Pure and Applied Algebra 51 (1988), 27-33 (with D. F. Anderson).
55. An existence theorem for non-Euclidean PID's, Communications in Algebra 16 (1988), 1221-1229.
56. Associated and weakly associated prime elements and primary decomposition in lattice modules, Algebra Universalis 25 (1988), 196-209 (with H. M. Nakkar).
57. Star operations induced by overrings, Communications in Algebra 16 (1988), 2535-2553.
58. On primary factorizations, Journal of Pure and Applied Algebra 54 (1988), 141-154 (with L. A. Mahaney).
59. Generating sets for ideals, Commentariorum Mathematicorum Universitatis Sancti Pauli 37 (1988), 173-177 (with L. A. Mahaney).
60. Pseudo-Dedekind domains and divisorial ideals in R[X]T, Journal of Algebra 122 (1989), 323-336 (with B. G. Kang).
61. Some quotient based statements in multiplicative ideal theory, Bollettino della Unione Matematica Italiana (7)3-B (1989), 455-476 (with J. L. Mott and M. Zafrullah).
62. Some characterizations of v-domains and related properties, Colloquium Mathematicum 58 (1989), 1-9 (with D. F. Anderson, D. L. Costa, D. E. Dobbs, J. L. Mott, and M. Zafrullah).
63. Localization of associated and weakly associated prime elements and supports of lattice modules of finite length, Studia Scientiarum Mathematicarum Hungarica 25 (1990), 263-273 (with H. M. Nakkar).
64. Dilworth's early papers on residuated and multiplicative lattices, The Dilworth Theorems, Birkhauser, Boston, 1990, 387-390.
65. Representation and embedding theorems for Noether lattices and r-lattices, The Dilworth Theorems, Birkhauser, Boston, 1990, 387-402.
66. Examples of star operations on integral domains, Communications in Algebra 18 (1990), 1621-1643 (with D. F. Anderson).
67. Factorization in integral domains, Journal of Pure and Applied Algebra 69 (1990), 1-19 (with D. F. Anderson and M. Zafrullah).
68. Weakly factorial domains and groups of divisibility, Proceedings of the American Mathematical Society 109 (1990), 907-913 (with M. Zafrullah).
69. Almost Bézout domains, Journal of Algebra 142 (1991), 285-309 (with M. Zafrullah).
70. Rings between D[X] and K[X], Houston Journal of Mathematics 17 (1991), 109-129 (with D. F. Anderson and M. Zafrullah).
71. Splitting the t-class group, Journal of Pure and Applied Algebra 74 (1991), 17-37 (with D. F. Anderson and M. Zafrullah).
72. Integral domains with finitely generated groups of divisibility, Proceedings of the American Mathematical Society 112 (1991), 613-618.
73. Atomic domains in which almost all atoms are prime, Communications in Algebra 20 (1992), 1447-1462 (with D. F. Anderson and M. Zafrullah).
74. Cohen-Kaplansky domains: integral domains with a finite number of irreducible elements, Journal of Algebra 148 (1992), 17-41 (with J. L. Mott).
75. Factorization in integral domains, II, Journal of Algebra 152 (1992), 78-93 (with D. F. Anderson and M. Zafrullah).
76. Finite character representations for integral domains, Bollettino della Unione Matematica Italiana (7)6-B (1992), 613-630 (with J. L. Mott and M. Zafrullah).
77. Elasticity of factorizations in integral domains, Journal of Pure and Applied Algebra 80 (1992), 217-235 (with D. F. Anderson).
78. Finitely generated monoids of fractional ideals, Communications in Algebra 21 (1993), 615-634 (with J. L. Mott and J. Park).
79. Rational elasticity of factorizations in Krull domains, Proceedings of the American Mathematical Society 117 (1993), 37-43 (with D. F. Anderson, S. Chapman and W. W. Smith).
80. t-linked extensions, the t-class group, and Nagata's Theorem, Journal of Pure and Applied Algebra 86 (1993), 109-124 (with E. G. Houston and M. Zafrullah).
81. Beck's coloring of a commutative ring, Journal of Algebra 159 (1993), 500-514 (with M. Naseer).
82. t-invertibility, III, Communications in Algebra 21 (1993), 1189-1201 (with M. Zafrullah).
83. On the lattice of ideals of a polynomial semiring, Algebra Universalis 31 (1994), 147-149 (with F. Alarcon).
84. Ideals generated by powers of elements, Bulletin of the Australian Mathematical Society 49 (1994), 373-376 (with K. R. Knopp and R. Lewin).
85. Elasticity of factorizations in integral domains, II, Houston Journal of Mathematics 20 (1994), 1-15 (with D. F. Anderson).
86. Baer lattices, Acta Scientiarum Mathematicarum 59 (1994), 61-74 (with C. Jayaram and P. A. Phiri).
87. Almost Bézout domains, II, Journal of Algebra 167 (1994), 547-556 (with K. R. Knopp and R. Lewin).
88. Sur les factorisations primaires réduites, Revue Roumaine de Mathematiques Pures et Appliques 39 (1994), 187-196 (with M. Ouhilal).
89. A note on minimal prime ideals, Proceedings of the American Mathematical Society 122 (1994), 13-14.
90. On a theorem of Kaplansky, Bollettino della Unione Matematica Italiana 8-A (1994), 397-402 (with M. Zafrullah).
91. Commutative semirings and their lattices of ideals, Houston Journal of Mathematics 20 (1994), 571-590 (with F. Alarcon).
92. The ring R[X,r/X], Zero-Dimensional Commutative Rings (eds. D.F. Anderson and D.E. Dobbs), Marcel Dekker, New York, 1995, 95-113 (with D.F. Anderson).
93. P.M. Cohn's completely primal elements, Zero-Dimensional Commutative Rings (eds. D.F. Anderson and D.E. Dobbs), Marcel Dekker, New York, 1995, 115-123 (with M. Zafrullah).
94. Some problems in commutative ring theory, Zero-Dimensional Commutative Rings (eds. D.F. Anderson and D.E. Dobbs), Marcel Dekker, New York, 1995, 363-372.
95. Some results on abstract commutative ideal theory, Periodica Mathematica Hungarica 30 (1995), 1-26 (with F. Alarcon and C. Jayaram).
96. Regular lattices, Studia Scientiarum Mathematicarum Hungarica 30 (1995), 379-388 (with C. Jayaram).
97. Noetherian rings with many more elements than height-one primes, Proceedings of the American Mathematical Society 123 (1995), 2971-2974.
98. A generalization of unique factorization, Bollettino della Unione Matematica Italiana 9-A (1995), 401-413 (with D. F. Anderson and M. Zafrullah).
99. Characterization of a class of r-lattices, Algebra Univeralis 33 (1995), 548-552 (with E. W. Johnson).
100. Agreeable domains, Communications in Algebra 23 (1995), 4861-4883 (with D.J. Kwak and M. Zafrullah).
101. Finite factorization domains, Proceedings of the American Mathematical Society 124 (1996), 389-396 (with B. Mullins).
102. Content formulas for polynomials and power series and complete integral closure, Journal of Algebra 181 (1996), 82-94 (with B.G. Kang).
103. Factorization in commutative rings with zero divisors, Rocky Mountain Journal of Mathematics 26 (1996), 439-480 (with S. Valdes-Leon).
104. Principal element lattices, Czechoslovak Mathematical Journal 46 (1996), 99-109 (with C. Jayaram).
105. The u, u-1 lemma revisited, Communications in Algebra 24 (1996), 2447-2454 (with D.J. Kwak).
106. Dilworth's principal elements, Algebra Universalis 36 (1996), 392-404 (with E.W. Johnson).
107. Quotients of unit groups of commutative rings, Commutative Ring Theory: Proceedings of the II International Conference (eds. P.-J. Cahen, M. Fontana, E. Houston and S.-E. Kabbaj), Marcel Dekker, New York, 1997, 15-25 (with B. Mullins).
108. Some remarks on G-Noetherian rings, Commutative Ring Theory: Proceedings of the II International Conference (eds. P.-J. Cahen, M. Fontana, E. Houston and S.-E. Kabbaj), Marcel Dekker, New York, 1997, 27-31 (with D.J. Kwak).
109. Some generalizations of GCD-domains, Factorization in Integral Domains (ed. D.D.Anderson), Marcel Dekker, New York, 1997, 189-195 (with R. Quintero).
110 Factorization in commutative rings with zero divisors, II, Factorization in Integral Domains (ed. D.D. Anderson), Marcel Dekker, New York, 1997, 197-219 (with S. Valdes-Leon).
111. On t-invertibility, IV, Factorization in Integral Domains (ed. D.D. Anderson), Marcel Dekker, New York, 1997, 221-225 (with M. Zafrullah).
112. Finitely generated multiplicative subsemigroups of rings, Semigroup Forum 55 (1997), 294-298.
113. A characterization of cancellation ideals, Proceedings of the American Mathematical Society 125 (1997), 2853-2854 (with M. Roitman).
114. Formally integrally closed domains and the rings R((X)) and R{{X}}, Journal of Algebra 200 (1998), 347-362 (with B.G. Kang).
115. Integral domains with highly nonunique factorization, Results in Mathematics 33 (1998), 22-29 (with S.T. Chapman and D.J. Kwak).
116. Criteria for unique factorization in integral domains, Journal of Pure and Applied Algebra 127 (1998), 205-218 (with S.T. Chapman, F. Halter-Koch and M. Zafrullah).
117. Armendariz rings and Gaussian rings, Communications in Algebra 26 (1998), 2265-2272 (with V. Camillo).
118. Anti-Archimedean rings and power series rings, Communications in Algebra 26 (1998), 3223-3238 (with B.G. Kang and M.H. Park).
119. Unique factorization rings with zero divisors, Communications in Algebra 27 (1999), 1967-1974. (with A.G. Agargun and S. Valdes-Leon).
120. p-domains without identity, Advances in Commutative Ring Theory (eds. D.E. Dobbs, M. Fontana, and S-.E Kabbaj), Marcel Dekker, New York, 1999, 25-30.
121. Extensions of unique factorization: A survey, Advances in Commutative Ring Theory, (eds. D.E. Dobbs, M. Fontana, and S-.E Kabbaj), Marcel Dekker, New York, 1999, 31-53.
122. GCD-sets in integral domains, Houston Journal of Mathematics 25 (1999), 15-34. (with D.F. Anderson and J. Park).
123. Semigroups and rings whose zero products commute, Communications in Algebra 27 (1999), 2847-2852 (with V. Camillo).
124. Star operations and primitive polynomials, Communications in Algebra 27 (1999), 3137-3142 (with M. Zafrullah).
125. Unique factorization in non-atomic integral domains, Bollettino della Unione Matematica Italiana 8 (2-B) (1999), 341-352 (with J.L. Mott and M. Zafrullah).
126. Independent locally finite intersections of localizations, Houston Journal of Mathematics 25 (1999), 433-452 (with M. Zafrullah).
128. Commutative rings with finitely generated multiplicative semigroup, Semigroup Forum 60 (2000), 436-443 (with J. Stickles).
129. Two star operations and their induced lattices, Communications in Algebra 28 (2000), 2461-2475 (with S. Cook).
130. Some remarks on multiplication ideals, II, Communications in Algebra 28 (2000), 2577-2583.
131. GCD domains, Gauss' Lemma, and content of polynomials, Non-Noetherian Commutative Ring Theory (eds. S. Chapman and S. Glaz), Mathematics and Its Applications, vol 520,
Kluwer Academic Publishers, Dordrecht/Boston/London, 2000, 1-31.
132. Factorization in commutative rings with zero divisors, III, Rocky Mountain Journal of Mathematics 31 (2001), 1-21 (with A.G. Agargun and S. Valdes-Leon).
133. Cancellation modules and related modules, Ideal Theoretic Methods in Commutative Algebra (eds. D.D. Anderson and I. Papick), Marcel Dekker, New York, 2001, 13-25.
134. Abstract ideal theory from Krull to the present, Ideal Theoretic Methods in Commutative Algebra (eds. D.D. Anderson and I. Papick), Marcel Dekker, New York, 2001, 27-47 (with
E.W. Johnson).
135. Splitting sets in integral domains, Proceedings of the American Mathematical Society 129 (2001), 2209-2217 (with M. Zafrullah).
136. Book review of Ideal Systems, An Introduction to Multiplicative Ideal Theory by F. Halter-Koch, Dekker, 1998, Jahresbericht der Deutschen Mathematiker-Vereingung
103 (2001), 34-35.
137. The ring D + XDS[X] and t-splitting sets, The Arabian Journal of Science and Engineering 26 (2001), 3-16 (with D.F. Anderson and M. Zafrullah).
139. Sublattices of regular elements, Periodica Mathematica Hungarica 44 (2002), 111-126 (with E.W. Johnson and R.L. Spellerberg).
140. Commutative rings whose elements are a sum of a unit and an idempotent, Communications in Algebra 30 (2002), 3327-3336 (with V. Camillo).
141. Multiplication modules and the ideal q(M), Communications in Algebra 30 (2002), 3383-3390 (with Y. Al-Shaniafi).
142. Some remarks on distinguished domains, International Journal of Commutative Rings 1 (2002), 43-50 (with D.J. Kwak and M. Zafrullah).
144. GCD domains and power series rings, Communications in Algebra 30 (2002), 5955-5960 (with B.G. Kang and M.H.Park).
145. Condensed domains, Canadian Mathematical Bulletin 46 (2003), 3-13 (with T. Dumitrescu).
149. Annihilator-semigroup rings, Tamkang Journal of Mathematics 34 (2003), 223-229 (with V. Camillo).
152. A note on almost GCD monoids, Semigroup Forum 69 (2004), 141-154 (with M. Zafrullah).
153. When are associates unit multiples, Rocky Mountain Journal of Mathematics 34 (2004), 811-828 (with M. Axtell, S.J. Forman and J. Stickles).
154. Half condensed domains, Houston Journal of Mathematics 30 (2004), 929-936 (with T. Dumitrescu).
155. Bases for modules, Expositiones Mathematicae 22 (2004), 283-296 (with J. Robeson).
156. Non-atomic unique factorization in integral domains, Arithmetical Properties of Commutative Rings and Monoids (S. Chapman, ed.), CRC Press, Boca Raton, 2005, 1-21.
158. Star-operations that distribute over finite intersections, Communications in Algebra 32 (2005), 2263-2274 (with S. Clarke).
159. Condensed rings with zero-divisors, Communications in Algebra 33 (2005), 3967-3976 (with T. Dumitrescu).
160. Weakly clean rings and almost clean rings, Rocky Mountain Journal of Mathematics 30 (2006), 783-798 (with M. Ahn).
162. When the v-operation distributes over intersections, Communications in Algebra 34 (2006), 4327-4337 (with S. Clarke).
163. Abstract ideal theory: multiplicative lattices and x-systems, International Journal of Algebra and Game Theory, 15 (2006), 27-35.
164. The Schreier property and Gauss’ Lemma, Bollettino della Unione Matematica Italiana (8) 10-B (2007), 43-62 (with M. Zafrullah).
165. Pseudo almost integral elements, Communications in Algebra 35 (2007), 1127-1131(with M. Zafrullah).
166. Quasi-Schreier domains, II, Communications in Algebra (to appear) (10 typed pages) (with T. Dumitrescu and M. Zafrullah).
167. Idealization of a module, Rocky Mountain Journal of Mathematics (in press) (54 pages in press) (with M. Winders).
168. Generalized ZPI-rings without identity, Houston Journal of Mathematics (to appear) (4 typed pages) (with J.S. Kintzinger).
169. Monoid domain constructions of antimatter domains, Communications in Algebra (to appear) (6 typed pages) (with J. Coykendall, L. Hill, and M. Zafrullah).
170. Bounded factorization rings, Communications in Algebra (to appear) (11 typed pages) (with A. Ganatra).
171. Generalizations of prime ideals, Communications in Algebra (to appear) (12 typed pages) (with M. Bataineh).
172. Annihilator semigroups and rings, Houston Journal of Mathematics (11 typed pages) (with S. Chun).
173. On a general theory of factorization in integral domains (submitted) (30 typed pages) (with A. Frazier).
174. Subgroups of direct products of groups, ideals and subrings of direct products of rings, and Goursat’s Lemma (submitted) (13 typed pages) (with V. Camillo).
175. Almost Bezout domains, III (submitted) (5 typed pages) (with M. Zafrullah).