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Original Articles

Radically Perfect Prime Ideals in Polynomial Rings Over Prüfer and Pullback Rings

Pages 1377-1385 | Received 23 Jun 2011, Published online: 02 Apr 2013

REFERENCES

  • Anderson , D. D. , Bouvier , A. , Dobbs , D. , Fontana , M. Kabbaj , S. ( 1988 ). On Jaffard domains . Exposition. Math. 6 ( 2 ): 145 – 175 .
  • Anderson , D. D. , Zafrullah , M. ( 1993 ). On t-invertibility III . Comm. Algebra 21 : 1189 – 1201 .
  • Bastida , E. , Gilmer , R. ( 1992 ). Overrings and divisorial ideals of rings of the form D+ M . Michigan Math. J. 20 : 79 – 95 .
  • Cowsik , R. C. , Nori , M. V. ( 1978 ). Affine curves in characteristic p are set-theoretic complete intersections . Invent. Math. 45 : 111 – 114 .
  • Eisenbud , D. , Evans , E. G. ( 1973 ). Every algebraic set in n-space is the intersection of n hypersurfaces . Invent. Math. 19 : 107 – 112 .
  • Erdogdu , V. ( 2004 ). Coprime packedness and set theoretic complete intersection of ideals in polynomial rings . Proc. Amer. Math. Soc. 132 : 3467 – 3471 .
  • Erdogdu , V. ( 2009 ). Radically perfect prime ideals in polynomial rings . Arch. Math. 93 : 213 – 217 .
  • Erdogdu , V. ( 2010 ). Efficient generation of prime ideals in polynomial rings up to radical . Comm. Algebra 38 ( 5 ): 1802 – 1807 .
  • Erdogdu , V. , Harman , S. Commutative rings whose prime ideals are radically perfect . J. Comm. Algebra , to appear .
  • Fontana , M. ( 1980 ). Topologically defined classes of Commutative rings . Ann. Mat. Pura Appl. 123 : 331 – 355 .
  • Fontana , M. , Gabelli , S. ( 1996 ). On the class group and local class group of a pullback . J. Algebra 181 : 803 – 835 .
  • Fontana , M. , Gabelli , S. , Houston , E. (1998). UMT-domains and domains with Prfer integral closure. Comm. Algebra 26:1017–1039.
  • Fontana , M. , Huckaba , J. , Papick , I. ( 1997 ). Prüfer Domains . Monographs and Text Books in Pure and Applied Mathematics 203. New York : M. Dekker .
  • Gabelli , S. , Houston , E. ( 1997 ). Coherentlike conditions in pullbacks . Michigan Math. J. 44 : 99 – 122 .
  • Gilmer , R. ( 1972 ). Multiplicative Ideal Theory . New York : Marcl Dekker .
  • Hamann , E. , Houston , E. , Johnston , J. ( 1988 ). Properties of uppers to zero in R[x] . Pac. J. Math. 135 : 65 – 79 .
  • Houston , E. ( 2006 ). Uppers to Zero in Polynomial Rings, Multiplicative Ideal Theory, In Commutative Algebra . New-York : Springer, pp. 243–261 .
  • Houston , E. , Zafrullah , M. ( 1989 ). On t-invertibility II . Comm. Algebra 17 ( 8 ): 1955 – 1969 .
  • Kunz , E. ( 1985 ). Introduction to Commutative Algebra and Algbraic Geometry . Boston : Birkhäuser .
  • Lyubeznik , G. ( 1992 ). The number of defining equations of affine algebraic sets . Amer. J. Math. 114 : 413 – 463 .
  • Communicated by I. Swanson.

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