Skip to main content
SpringerLink
Log in

RRF rings which are not LRF

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring\(T = \left( \begin{gathered} A0 \hfill \\ MB \hfill \\ \end{gathered} \right)\) to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF.

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. Goodearl K R, Surjective endomorphisms of finitely generated modules,Comm. Algebra 15 (1987) 589–609

    Article  MATH  MathSciNet  Google Scholar 

  2. Green E L, On the representation theory of rings in matrix form,Pacific J. Math. 100 (1982) 123–138

    MATH  MathSciNet  Google Scholar 

  3. Haghany A and Varadarajan K, Study of modules over formal triangular matrix rings, to appear inJ. Pure Appl. Algebra (2000)

  4. Herstein I N, A counterexample in Noetherian rings,Proc. Natl. Acad. Sci. U.S.A. 54 (1965) 1036–1037

    Article  MATH  MathSciNet  Google Scholar 

  5. Hirano Y, On rings over which each module has a maximal submodule, Preprint

  6. Hirano Y, Rings in which the injective hulls of simple modules have finiteness conditions, Preprint

  7. Muller Marianne, Rings of quotients of generalized matrix rings,Comm. Algebra 15 (1987) 1991–2015

    Article  MathSciNet  Google Scholar 

  8. Stenstrom B, The maximal ring of quotients of a generalised matrix ring, Universale Algebren und theorie der radikale, Studien zur Algebra und ihre Anwendungen (Akademie-Verlag, Berlin) (1976) pp. 65–67

    Google Scholar 

  9. Varadarajan K, Residual finiteness in rings and modules,J. Ramanujan Math. Soc. 8 (1993) 29–48

    MATH  MathSciNet  Google Scholar 

  10. Varadarajan K, Rings with all modules residually finite,Proc. Indian Acad. Sci. (Math. Sci.) 109 (1999) 345–351

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    K. Varadarajan

Authors
  1. K. Varadarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Varadarajan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Varadarajan, K. RRF rings which are not LRF. Proc. Indian Acad. Sci. (Math. Sci.) 110, 133–136 (2000). https://doi.org/10.1007/BF02829487

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02829487

Keywords

Search

Navigation