63
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Note on Star Operations Over Polynomial Rings

Pages 4249-4256 | Received 10 May 2007, Published online: 02 Dec 2008

REFERENCES

  • Anderson , D. D. , Cook , S. J. ( 2000 ). Two star-operations and their induced lattices . Comm. Algebra 28 ( 5 ): 2461 – 2475 .
  • Anderson , D. D. , Clarke , S. M. ( 2005 ). Star-operations that distribute over finite intersections . Comm. Algebra 32 : 2263 – 2274 .
  • Anderson , D. D. , Clarke , S. M. ( 2006 ). When the v-operation distributes over intersections . Comm. Algebra 34 : 4327 – 4337 .
  • Bastida , E. , Gilmer , R. ( 1992 ). Overrings and divisorial ideals of rings of the form D + M . Michigan Math. J. 20 : 79 – 95 .
  • Dobbs , D. , Houston , E. , Lucas , T. , Zafrullah , M. ( 1989 ). t-linked overrings and Prüfer v-multiplication domains . Comm. Algebra 17 : 2835 – 2852 .
  • Dobbs , D. , Houston , E. , Lucas , T. , Roitman , M. , Zafrullah , M. ( 1992 ). On t-linked overrings . Comm. Algebra 20 : 1463 – 1488 .
  • Fanggui , W. ( 2004 ). On induced operations and UMT-domains . Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 27 ( 1 ): 1 – 9 .
  • Fontana , M. , Huckaba , J. Localizing systems and semistar operations . In: Chapman , S. , Glaz , S. , eds. Non Noetherian Commutative Ring Theory . Chapter 8 . Dordrecht : Kluwer Academic Publishers , pp. 169 – 187 .
  • Fontana , M. , Loper , K. ( 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. M. Dekker, pp. 189 – 206 .
  • Fontana , M. , Loper , K. ( 2003 ). Nagata rings, Kronecker function rings, and related semistar operations . Comm. Algebra 31 ( 10 ): 4775 – 4805 .
  • Fontana , M. , Gabelli , S. , Houston , E. ( 1998 ). UMT-domains and domains with Prüfer integral closure . Comm. Algebra 26 ( 4 ): 1017 – 1039 .
  • Gilmer , R. ( 1972 ). Multiplicative ideal theory . Pure and Applied Mathematics , 12 . New York : Marcel Dekker, Inc .
  • Hedstrom , J. , Houston , E. ( 1980 ). Some remarks on star-operations . J. Pure Appl. Algebra 18 : 37 – 44 .
  • Houston , E. , Zafrullah , M. ( 1989 ). On t-invertibility II . Comm. Algebra 17 : 1955 – 1969 .
  • Houston , E. , Zafrullah , M. ( 2005 ). UMV-Domains, Arithmetical Properties of Commutative Rings and Monoids . Lect. Notes Pure Appl. Math. 241 Boca Raton , FL : Chapman & Hall/CRC , pp. 304 – 315 .
  • Houston , E. , Malik , S. , Mott , J. ( 1984 ). Characterizations of *-multiplication domains . Canad. Math. Bull. 27 : 48 – 52 .
  • Kaplansky , I. ( 1974 ). Commutative Rings . Chicago : The University of Chicago Press .
  • Communicated by I. Swanson.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.