Skip to main content
SpringerLink
Log in

Distributive semiprime rings

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx n A=Ax n. We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Tuganbaev, “Distributive rings and modules,”Mat. Zametki [Math. Notes],47, No. 2, 115–123 (1990).

    MATH  MathSciNet  Google Scholar 

  2. A. A. Tuganbaev, “Distributive rings,”Mat. Zametki [Math. Notes],35, No. 3, 329–332 (1984).

    MATH  MathSciNet  Google Scholar 

  3. C. Faith,Algebra: Rings, Modules, and Categories, Vol. 1, Springer-Verlag, New York-Heidelberg (1973).

    Google Scholar 

  4. A. A. Tuganbaev, “Left and Right Distributive Rings,”Mat. Zametki [Math. Notes],58, No. 4, 604–627 (1995).

    MATH  MathSciNet  Google Scholar 

  5. V. A. Andrunakievich and Yu. M. Ryabukhin,Radicals of Algebras and Structure Theory [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  6. L. H. Rowen,Ring Theory. Student Edition, Academic Press, Boston (1991).

    Google Scholar 

  7. B. Stenström,Rings of Quotients: an Introduction to Methods of Ring Theory, Springer-Verlag, Berlin (1975).

    Google Scholar 

  8. P. Kohn,Free Rings and Their Relations, Academic Press, London (1971).

    Google Scholar 

  9. F. Kasch,Modulen und Ringe, Mathematische Leitfäden, B. G. Teubner, Stuttgart (1977).

    Google Scholar 

  10. C. Faith,Algebra: Rings, Modules, and Categories, Vol. 2, Springer-Verlag, New York-Heidelberg (1973).

    Google Scholar 

  11. W. D. Burgess and W. Stephenson, “An analogue of the Pierce sheaf for non-commutative rings,”Comm. Algebra,6, No. 9, 863–886 (1978).

    MathSciNet  Google Scholar 

  12. W. D. Burgess and W. Stephenson, “Rings all of whose Pierce stalks are local,”Canad. Math. Bull.,22, No. 2, 159–164 (1979).

    MathSciNet  Google Scholar 

  13. K. R. Goodearl,Von Neumann Regular Rings, Pitman, London (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Energy Institute, USSR

    A. A. Tuganbaev

Authors
  1. A. A. Tuganbaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 736–761, November, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tuganbaev, A.A. Distributive semiprime rings. Math Notes 58, 1197–1215 (1995). https://doi.org/10.1007/BF02305004

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02305004

Keywords

Search

Navigation