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Original Articles

Universally Catenarian Integral Domains, Strong S-Domains and Semistar Operations

Pages 673-683 | Received 29 May 2008, Published online: 18 Feb 2010

REFERENCES

  • Anderson , D. F. , Bouvier , A. , Dobbs , D. , Fontana , M. , Kabbaj , S. ( 1988 ). On Jaffard domain . Expo. Math. 6 : 145 – 175 .
  • Ayache , A. , Cahen , P. ( 1992 ). Anneaux verifiant absolument l'inegalité ou la formule de la dimension . Boll. Un. Mat. Ital. 6-B : 36 – 65 .
  • Bouvier , A. , Fontana , M. ( 1985 ). The catenary property of the polynomial rings over a Prüfer domain . In: Séminare d'Algèbre Paul Dubreil et Marie-Paule Malliavin . LNM., 1146 . New York : Springer-Verlag , pp. 340 – 354 .
  • Bouvier , A. , Dobbs , D. E. , Fontana , M. ( 1988 ). Universally catenarian integral domains . Advances in Math. 72 : 211 – 238 .
  • Bruns , W. , Herzog , J. ( 1998 ). Cohen–Macaulay Rings . Cambridge Studies in Advanced Mathematics, 39 . Cambridge : Cambridge University Press .
  • Brewer , J. , Montgomery , P. , Rutter , E. , Heinzer , W. ( 1973 ). Krull Dimension of Polynomial Rings . Conference on Commutative Algebra, LNM., 311 . New York : Springer-Verlag , pp. 26 – 45 .
  • Chang , G. W. , Fontana , M. ( 2009 ). Uppers to zero in polynomial rings and Prüfer-like domains . Comm. Algebra 37 : 164 – 192 .
  • Dobbs , D. E. , Papick , I. J. ( 1976 ). On going-down for simple overrings III . Proc. Amer. Math. Soc. 54 : 35 – 38 .
  • Dobbs , D. E. , Sahandi , P. ( 2009 ). Goin-down and Semistar operations . J. Algebra Appl. 8 ( 1 ): 83 – 104 .
  • El Baghdadi , S. , Fontana , M. ( 2004 ). Semistar linkedness and flatness, Prüfer semistar multiplication domains . Comm. Algebra 32 : 1101 – 1126 .
  • El Baghdadi , S. , Fontana , M. , Picozza , G. ( 2004 ). Semistar Dedekind domains . J. Pure Appl. Algebra 193 : 27 – 60 .
  • Fontana , M. , Huckaba , J. A. ( 2000 ). Localizing systems and semistar operations . In: Chapman , S. , Glaz , S. , eds. Non Noetherian Commutative Ring Theory . Dordrecht : Kluwer , pp. 169 – 197 .
  • Fontana , M. , Huckaba , J. , Papick , I. ( 1997 ). Prüfer Domains . New York : Marcel Dekker .
  • Fontana , M. , Jara , P. , Santos , E. ( 2003 ). Prüfer ★-multiplication domains and semistar operations . J. Algebra Appl. 2 : 21 – 50 .
  • Fontana , M. , Loper , K. A. ( 2003 ). Nagata rings, Kronecker function rings and related semistar operations . Comm. Algebra 31 : 4775 – 4801 .
  • Fontana , M. , Loper , K. A. ( 2001 ). Kronecker function rings: a general approach . In: Anderson , D. D. , Papick , I. J. , eds. Ideal Theoretic Methods in Commutative Algebra . Lecture Notes Pure Appl. Math. 220 . New York : Dekker , pp. 189 – 205 .
  • Gilmer , R. ( 1972 ). Multiplicative Ideal Theory . New York : Dekker .
  • Kaplansky , I. ( 1974 ). Commutative Rings. , Rev. ed. Chicago : University Chicago Press .
  • Malik , S. , Mott , J. L. ( 1983 ). Strong S-domains . J. Pure Appl. Algebra 28 : 249 – 264 .
  • Okabe , A. , Matsuda , R. ( 1994 ). Semistar-operations on integral domains . Math. J. Toyama Univ. 17 : 1 – 21 .
  • Ratliff , L. J. Jr. ( 1970 ). On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals, II . Amer. J. Math. 92 : 99 – 144 .
  • Sahandi , P. ( 2009 ). Semistar-Krull and valuative dimension of integral domains . Ricerche Mat. 58 : 219 – 242 .
  • Seidenberg , A. ( 1953 ). A note on the dimension theory of rings . Pacific J. Math. 3 : 505 – 512 .
  • Seidenberg , A. ( 1954 ). On the dimension theory of rings II . Pacific J. Math. 4 : 603 – 614 .
  • Communicated by I. Swanson.

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