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Original Articles

Semistar Linkedness and Flatness, Prüfer Semistar Multiplication Domains

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Pages 1101-1126 | Received 01 Oct 2002, Published online: 01 Feb 2007

References

  • Anderson , D. D. 1988 . Star-operations induced by overrings . Comm. Algebra , 16 : 2535 – 2553 .
  • Anderson , D. D. and Anderson , D. F. 1990 . Examples of star-operations on integral domains . Comm. Algebra , 18 : 1621 – 1643 .
  • Anderson , D. F. , Houston , E. G. and Zafrullah , M. 1991 . Pseudo-integrality . Canad. Math. Bull. , 34 : 15 – 22 .
  • Davis , E. 1964 . Overrings of commutative rings, II . Trans. Amer. Math. Soc. , 110 : 196 – 212 .
  • Dobbs , D. E. , Houston , E. G. , Lucas , T. G. and Zafrullah , M. 1989 . t-linked overrings and Prüfer v-multiplication domains . Comm. Algebra , 17 : 2835 – 2852 .
  • Dobbs , D. E. , Houston , E. G. , Lucas , T. G. , Roitman , M. and Zafrullah , M. 1992 . On t-linked overrings . Comm. Algebra , 20 : 1463 – 1488 .
  • Fontana , M. 1980 . Topologically defined classes of commutative rings . Annali Mat. Pura Appl. , 123 : 331 – 345 .
  • Fontana , M. and Huckaba , J. 2000 . “ Localizing systems and semistar operations ” . In Non Noetherian Commutative Ring Theory Edited by: Chapman , S. and Glaz , S. 169 – 197 . Kluwer Academic Publishers . Chapter 8
  • Fontana , M. and Loper , K. A. 2001a . “ Kronecker function rings: a general approach ” . In Ideal Theoretic Methods in Commutative Algebra , M. Dekker Lecture Notes Pure Appl. Math. 220 Edited by: Anderson , D.D. and Papick , I.J. 189 – 206 .
  • Fontana , M. and Loper , K. A. 2001b . A Krull-type theorem for the semistar integral closure of an integral domain . AJSE Theme Issue “Commutative Algebra” , 26C : 89 – 95 .
  • Fontana , M. and Loper , K. A. 2003 . Nagata rings, Kronecker function rings and related semistar operations . Comm. Algebra , 31 : 4775 – 4805 .
  • Fontana , M. , Jara , P. and Santos , E. 2003 . Prüfer ⋆-multiplication domains and semistar operations . J. Algebra Appl. , 2 : 21 – 50 . [CROSSREF]
  • Fossum , R. M. 1973 . The Divisor Class Group of a Krull Domain Springer .
  • Garcia , J. M. , Jara , P. and Santos , E. 1999 . Prüfer ⋆-multiplication domains and torsion theories . Comm. Algebra , 27 : 1275 – 1295 .
  • Gilmer , R. 1972 . Multiplicative Ideal Theory Marcel Dekker .
  • Gilmer , R. and Heitmann , R. C. 1980 . On Pic(R[X]) for R seminormal . J. Pure Appl. Algebra , 16 : 251 – 257 . [CROSSREF]
  • Griffin , M. 1967 . Some results on v-multiplication rings . Canad. J. Math. , 19 : 710 – 721 .
  • Halter-Koch , F. 1998 . Ideal Systems. An Introduction to Multiplicative Ideal Theory New York : Marcel Dekker .
  • Halter-Koch , F. 1997 . “ Generalized integral closures ” . In Factorization in Integral Domains , M. Dekker Lect. Notes Math. Pure Appl. 187 Edited by: Anderson , D. D. 349 – 358 .
  • Halter-Koch , F. 2001 . Localizing systems, module systems, and semistar operations . J. Algebra , 238 : 723 – 761 . [CROSSREF]
  • Houston , E. G. , Malik , S. B. and Mott , J. L. 1984 . Characterization of ⋆-multiplication domains . Canad. Math. Bull. , 27 : 48 – 52 .
  • Jaffard , P. 1960 . Les Systèmes d'Idéaux Paris : Dunod .
  • Kang , B. G. 1989 . Prüfer v-multiplication domains and the ring . J. Algebra , 123 : 151 – 170 .
  • Kaplansky , I. 1970 . Commutative Rings Boston : Allyn and Bacon .
  • Krull , W. 1936 . Beiträge zur Arithmetik kommutativer Integritätbereiche, II . Mat. Z. , 41 : 665 – 679 .
  • Kwak , D. J. and Park , Y. S. 1995 . On t-flat overrings . Ch. J. Math. , 23 : 17 – 24 .
  • Matsuda , R. and Sato , I. 1996 . Note on star-operations and semistar operations . Bull. Fac. Sci. Ibaraki Univ. , 28 : 155 – 161 .
  • Matsuda , R. and Sugatani , T. 1995 . Semistar operations on integral domains II . J. Toyama Univ. , 18 : 155 – 161 .
  • Mott , J. L. and Zafrullah , M. 1981 . On Prüfer v-multiplication domains . Manuscripta Math. , 35 : 1 – 26 .
  • Okabe , A. and Matsuda , R. 1992 . Star operations and generalized integral closures . Bull. Fac. Sci. Ibaraki Univ. Ser. A , 24 : 7 – 13 .
  • Okabe , A. and Matsuda , R. 1994 . Semistar operations on integral domains . Math. J. Toyama Univ. , 17 : 1 – 21 .
  • Prüfer , H. 1932 . Untersuchungen über Teilbarkeitseigenschaften in Körpern . J. Reine Angew. Math. , 168 : 1 – 36 .
  • Richman , F. 1965 . Generalized quotient rings . Proc. Amer. Math. Soc. , 16 : 794 – 799 .
  • #Communicated by R. Villarreal.

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