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Original Articles

Star Operations on Overrings and Semistar Operations

Pages 2051-2073 | Received 01 Feb 2004, Accepted 15 Sep 2004, Published online: 01 Feb 2007

REFERENCES

  • Anderson , D. D. , Anderson , D. F. ( 1990 ). Examples of star operations on integral domains . Comm. Algebra 18 ( 5 ): 1621 – 1643 .
  • Arnold , J. T. , Brewer , J. W. ( 1971 ). On flat overrings, ideal transforms and generalized transforms of a commutative ring . J. Algebra 18 : 254 – 263 . [CROSSREF]
  • Bazzoni , S. , Salce , L. ( 1996 ). Warfield domains . J. Algebra 185 ( 3 ): 836 – 868 . [CROSSREF]
  • Bazzoni , S. ( 2000 ). Divisorial domains . Forum Math. 12 ( 4 ): 397 – 419 .
  • Dobbs , D. E. , Fedder , R. ( 1984 ). Conducive integral domains . J. Algebra 86 ( 2 ): 494 – 510 . [CROSSREF]
  • El Baghdadi , S. , Fontana , M. ( 2004 ). Semistar linkedness and flatness, Prüfer semistar multiplication domains . Comm. Algebra 32 ( 3 ): 1101 – 1126 . [CROSSREF]
  • Fontana , M. , Jara , P. , Santos , E. ( 2003 ). Prüfer ⋆-multiplication domains and semistar operations . J. Algebra Appl. 2 ( 1 ): 21 – 50 . [CROSSREF]
  • Fontana , M. , Huckaba , J. A. ( 2000 ). Localizing systems and semistar operations . In: Chapman , S. T. , Glaz , S. , eds. Non-Noetherian Commutative Ring Theory . Dordrecht : Kluwer Academic Publishers , pp. 169 – 198 .
  • Fontana , M. , Huckaba , J. A. , Papick , I. J. ( 1997 ) . Prüfer domains . New York : Marcel Dekker Inc .
  • Fontana , M. , Loper , K. A. ( 2001 ) . Kronecker function rings: a general approach . In: Ideal Theoretic Methods in Commutative Algebra . Lecture Notes in Pure and Appl. Math. 220 . New York : Dekker , pp. 189 – 205 .
  • Fontana , M. , Loper , K. A. ( 2003 ). Nagata rings, Kronecker function rings, and related semistar operations . Comm. Algebra 31 ( 10 ): 4775 – 4805 .
  • Fontana , M. , Park , M. H. ( 2004 ). Star operations and pullbacks . J. Algebra 274 ( 1 ): 387 – 421 . [CROSSREF]
  • Fontana , M. , Picozza , G. (to appear) . Semistar invertibility on integral domains . Algebra Colloq.
  • Gilmer , R. ( 1992 ) . Multiplicative Ideal Theory . Kingston , ON , Canada : Queen's University .
  • Glaz , S. , Vasconcelos , W. V. ( 1977 ). Flat ideals. II . Manuscripta Math. 22 ( 4 ): 325 – 341 . [CROSSREF]
  • Halter-Koch , F. ( 1998 ) . Ideal Systems . Monographs and Textbooks in Pure and Applied Mathematics. Vol. 211 . New York : Marcel Dekker Inc .
  • Halter-Koch , F. ( 2001 ). Localizing systems, module systems, and semistar operations . J. Algebra 238 ( 2 ): 723 – 761 . [CROSSREF]
  • Halter-Koch , F. ( 2003 ). Characterization of Prüfer multiplication monoids and domains by means of spectral module systems . Monatsh. Math. 139 ( 1 ): 19 – 31 . [CROSSREF]
  • Heinzer , W. ( 1968 ). Integral domains in which each non-zero ideal is divisorial . Mathematika 15 : 164 – 170 .
  • Heinzer , W. J. , Huckaba , J. A. , Papick , I. J. ( 1998 ). m -canonical ideals in integral domains . Comm. Algebra 26 ( 9 ): 3021 – 3043 .
  • Matsuda , R. ( 2000 ). Note on valuation rings and semistar-operations . Comm. Algebra 28 ( 5 ): 2515 – 2519 .
  • Matsuda , R. , Sugatani , T. ( 1995 ). Semistar-operations on integral domains. II . Math. J. Toyama Univ. 18 : 155 – 161 .
  • Matsumura , H. ( 1986 ). Commutative Ring Theory . Cambridge : Cambridge University Press.
  • Mimouni , A. (to appear) . Semistar Operations of Finite Character on Integral Domains . Journal of Pure and Applied Algebra .
  • Mimouni , A. , Samman , M. ( 2003 ). Semistar operations on valuation domains . Int. J. Comm. Rings 2 : 131 – 141 .
  • Okabe , A. , Matsuda , R. ( 1994 ). Semistar-operations on integral domains . Math. J. Toyama Univ. 17 : 1 – 21 .
  • Olberding , B. ( 1998 ). Globalizing local properties of Prüfer domains . J. Algebra 205 ( 2 ): 480 – 504 . [CROSSREF]
  • Uda , H. ( 1983 ). LCM-stableness in ring extensions . Hiroshima Math. J. 13 ( 2 ): 357 – 377 .
  • Wang , F. , McCasland , R. L. ( 1997 ). On w -modules over strong Mori domains . Comm. Algebra 25 ( 4 ): 1285 – 1306 .
  • #Communicated by A. Facchini.

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