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Original Articles

Module-Theoretic Characterizations of Generalized GCD Domains

Pages 759-772 | Received 19 May 2008, Published online: 18 Feb 2010

REFERENCES

  • Anderson , D. D. ( 1978 ). π-domains, divisorial ideals, overrings . Glasgow Math. J. 19 : 199 – 203 .
  • Anderson , D. D. , Anderson , D. F. ( 1979 ). Generalized GCD-domains . Comment. Math. Univ. St. Pauli 23 : 213 – 221 .
  • Anderson , D. D. , Anderson , D. F. , Zafrullah , M. ( 2001 ). The ring D + XD S [X] and t-splitting sets . Commutative Algebra Arabian J. Sci. Eng. Sect. C Theme Issues 26 : 3 – 16 .
  • Anderson , D. D. , Cook , S. J. ( 2000 ). Two star-operations and their induced lattices . Comm. Algebra 28 : 2461 – 2475 .
  • Anderson , D. D. , Dumitrescu , D. , Zafrullah , M. ( 2007 ). Quasi-Schreier domains II . Comm. Algebra 35 : 2096 – 2104 .
  • Anderson , D. D. , Houston , E. G. , Zafrullah , M. ( 1993 ). t-linked extensions, the t-class group, and Nagata's theorem . J. Pure Appl. Algebra 86 : 109 – 124 .
  • Anderson , D. F. ( 2000 ). The class group and local class group of an integral domain . In: Chapman , S. T. , Glaz , S. , eds. Non-Noetherian Commutative Ring Theory . Math. Appl. 520. Dordrecht : Kluwer Academic Publishers , pp. 33 – 55 .
  • Anderson , D. F. , El Abidine , D. N. ( 2001 ). The A + XB[X] and A + XB[[X]] constructions from GCD-domains . J. Pure Appl. Algebra 159 : 15 – 24 .
  • Anderson , D. F. , El Baghdadi , S. , Kabbaj , S. ( 1999 ). On the class group of A + XB[X] domains . In: Dobbs , D. E. , Fontana , M. , Kabbaj , S.-E. , eds. Advances in Commutative Ring Theory . Lecture Notes in Pure and Applied Mathematics , Vol. 205 . New York : Marcel Dekker , pp. 73 – 85 .
  • Arnold , J. T. , Brewer , J. W. ( 1971 ). On flat overrings, ideal transforms and generalized transforms of a commutative ring . J. Algebra 18 : 254 – 263 .
  • Bouvier , A. , Zafrullah , M. ( 1988 ). On some class groups of an integral domain . Bull. Soc. Math. Grece (N.S.) 29 : 45 – 59 .
  • Bourbaki , N. ( 1989 ). Commutative Algebra . New York : Springer-Verlag .
  • Butts , H. S. , Spaht , C. G. ( 1972 ). Generalized quotient rings . Math. Nachr. 53 : 181 – 210 .
  • Dobbs , D. E. , Houston , E. G. , Lucas , T. G. , Roitman , M. , Zafrullah , M. ( 1992 ). On t-linked overrings . Comm. Algebra 20 : 1463 – 1488 .
  • Dobbs , D. E. , Houston , E. G. , Lucas , T. G. , Zafrullah , M. ( 1989 ). t-linked overrings and Prüfer v-multiplication domains . Comm. Algebra 17 : 2835 – 2852 .
  • Fontana , M. , Gabelli , S. (1996). On the class group and the local class group of a pullback. J. Algebra 181:803–835.
  • Fuchs , L. ( 2003 ). Injective modules over Mori domains . Studia Sci. Math. Hungar. 40 : 33 – 40 .
  • Fuchs , L. , Salce , L. ( 2001 ). Modules over Non-Noetherian Domains . Mathematical Surveys and Monographs , Vol. 84 . Providence , RI : AMS .
  • Gilmer , R. ( 1992 ). Multiplicative Ideal Theory . Queen's Papers in Pure and Applied Mathematics , Vol. 90 . Kingston , Ontario : Queen's University .
  • Glaz , S. , Vasconcelos , W. V. ( 1977 ). Flat ideals II . Manuscripta Math. 22 : 325 – 341 .
  • Hedstrom , J. R. , Houston , E. G. ( 1980 ). Some remarks on star-operations . J. Pure Appl. Algebra 18 : 37 – 44 .
  • Houston , E. G. , Taylor , J. ( 2007 ). Arithmetic properties in pullbacks . J. Alg. 310 : 235 – 260 .
  • Kang , B. G. ( 1989 ). On the converse of a well known fact about Krull domains . J. Alg. 124 : 284 – 299 .
  • Kang , B. G. ( 1989 ). Prüfer v-multiplication domains and the ring R[X] N v . J. Alg. 123 : 151 – 170 .
  • Kim , H. ( 2008 ). Module-theoretic characterizations of t-linkative domains . Comm. Algebra 36 : 1649 – 1670 .
  • Kim , H. , Kim , E. S. , Park , Y. S. ( 2008 ). Injective modules over strong Mori domains . Houston J. Math. 34 : 349 – 360 .
  • Kwak , D. J. , Park , Y. S. ( 1995 ). On t-flat overrings . Chinese J. Math. 23 : 17 – 24 .
  • Lam , T. Y. ( 1998 ). Lectures on Modules and Rings . GTM 189 . New York : Springer-Verlag .
  • Mimouni , A. ( 1999 ). Pullbacks and coherent-like properties . In: Dobbs , D. E. , Fontana , M. , Kabbaj , S.-E. , eds. Advances in Commutative Ring Theory . Lect. Notes Pure Appl. Math. , Vol. 205 . New York : Dekker , pp. 437 – 459 .
  • Mimouni , A. ( 2005 ). Integral domains in which each ideal is a w-ideal . Comm. Algebra 33 : 1345 – 1355 .
  • Richman , F. ( 1965 ). Generalized quotient rings . Proc. Am. Math. Soc. 16 : 794 – 799 .
  • Rotman , J. J. ( 1993 ). An Introduction to Homological Algebra . San Diego : Academic Press .
  • Uda , H. ( 1983 ). LCM-stableness in ring extensions . Hiroshima Math. J. 13 : 357 – 377 .
  • Wang , F. , McCasland , R. L. ( 1997 ). On w-modules over strong Mori domains . Comm. Algebra 25 : 1285 – 1306 .
  • Wang , F. , McCasland , R. L. ( 1999 ). On strong Mori domains . J. Pure Appl. Algebra 135 : 155 – 165 .
  • Zafrullah , M. ( 1987 ). On a property of pre-Schreier domains . Comm. Algebra 15 : 1895 – 1920 .
  • Zafrullah , M. ( 1990 ). Flatness and invertiblity of an ideal . Comm. Algebra 18 : 2151 – 2158 .
  • Communicated by A. Singh.
  • Dedicated to Evan G. Houston on the occasion of his sixtieth birthday.

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