Advertisement

Israel Journal of Mathematics

, Volume 37, Issue 4, pp 315–326 | Cite as

Zariski extensions and biregular rings

  • E. Nauwelaerts
  • F. Van Oystaeyen
Article

Abstract

In this paper we study the structure of Zariski central rings with regular center i.p. biregular rings, and we obtain structure theorems for algebras which are finitely generated over their regular center, etc. Characterizations of certain classes of rings are being obtained by using localization at prime ideals and local-global theorems.

Keywords

Prime Ideal Regular Ring Semiprime Ring Artinian Ring Simple Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. P. Armendariz,On semiprime P.I. algebras over commutative regular rings, Pacific J. Math.66 (1976), 23–28.MATHMathSciNetGoogle Scholar
  2. 2.
    E. P. Armendariz and J. W. Fisher,Regular P.I.-Rings, Proc. Amer. Math. Soc.39 (1973), 247–251.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    E. P. Armendariz, J. W. Fisher and S. A. Steinberg,Central localizations of regular rings, Proc. Amer. Math. Soc.46 (1974), 315–321.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    C. Faith,Algebra: Rings, Modules and Categories I, Springer-Verlag, Berlin-Heidelberg-New York, 1973.MATHGoogle Scholar
  5. 5.
    J. W. Fisher,Von Neumann regular rings versus V-rings, inRing Theory, Proc. Univ. of Oklahoma Conference, M. Dekker Inc., New York, 1974, pp. 101–119.Google Scholar
  6. 6.
    J. W. Fisher and R. L. Snider,On the Von Neumann regularity of rings with regular prime factor rings, Pacific J. Math.54 (1974), 135–144.MATHMathSciNetGoogle Scholar
  7. 7.
    O. Goldman,Rings and modules of quotients, J. Algebra13 (1969), 10–47.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Lambek and G. Michler,The torsion theory at a prime ideal of a right Noetherian rings, J. Algebra25 (1973), 364–389.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    G. O. Michler and O. E. Villamayor,On rings whose simple modules are injective, J. Algebra25 (1973), 185–201.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    B. Mueller,Localization of Non-commutative Noetherian Rings at Semiprime Ideals, Lecture Notes, McMaster University, 1974.Google Scholar
  11. 11.
    D. C. Murdoch and F. Van Oystaeyen,Noncommutative localization and sheaves, J. Algebra35 (1975), 500–515.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    B. Osofsky,On twisted polynomial rings, J. Algebra18 (1971), 597–607.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    C. Procesi,Rings with polynomial identities, inPure and Applied Math., Vol. 17, M. Dekker Inc. New York, 1973.Google Scholar
  14. 14.
    J. C. Robson and L. Small,Idempotent ideals in P.I. rings, J. London Math. Soc.14 (1976), 120–122.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    J. Van Geel and F. Van Oystaeyen,Local-global results for regular rings, Comm. Algebra4 (1976), 811–821.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    F. Van Oystaeyen,Prime Spectra in Non-commutative Algebra, Lecture Notes in Math.444, Springer-Verlag, Berlin-Heidelberg-New York, 1975.MATHGoogle Scholar
  17. 17.
    F. Van Oystaeyen,Zariski central rings, Comm. Algebra6 (1978), 799–821.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    F. Van Oystaeyen,Birational ring homomorphisms and ring extensions, inRing Theory, Proc. 1977 Conference, Lecture Notes, Vol. 40, M. Dekker Inc., New York, 1978, pp. 155–179.Google Scholar

Copyright information

© Hebrew University 1980

Authors and Affiliations

  • E. Nauwelaerts
    • 1
    • 2
  • F. Van Oystaeyen
    • 1
    • 2
  1. 1.Department of MathematicsL. U. C. HasseltBelgium
  2. 2.Department of MathematicsUniversity of AntwerpBelgium

Personalised recommendations