Skip to main content
SpringerLink
Log in

The Maximal Graded Left Quotient Algebra of a Graded Algebra1)

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A–modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.

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. Utumi, Y.: On quotient rings. Osaka J. Math., 8, 1–18 (1956)

    MathSciNet  Google Scholar 

  2. Beidar, K. I., Martindale III, W. S., Mikhalev, A. V.: Rings with generalized identities. Pure and Applied Mathematics, 196, Marcel Dekker, Inc., 1996

  3. Lam, T. Y.: Lectures on Modules and Rings, Graduate texts in Mathematics, 189, Springer-Verlag, New York, 1999

  4. Lambek, J.: Lectures on Rings and Modules. Chelsea Publishing Company, New York, 1976

  5. Stenström, B.: Rings of quotients, Springer-Verlag, New York, 1975

  6. McCrimmon, K.: Martindale systems of symmetric quotients. Algebras, Groups and Geometries, 6, 153–237 (1989)

    MATH  MathSciNet  Google Scholar 

  7. Schelter, W.: Two sided rings of quotients. Arch. Math., 24, 274–277 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gómez Lozano, M., Siles Molina, M.: Quotient rings and Fountain–Gould left orders by the local approach. Acta Math. Hungar., 97, 287–301 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. van Oystaeyen, F.: On graded rings and modules of quotients. Comm. in Algebra, 6(8), 1923–1959 (1978)

    MATH  MathSciNet  Google Scholar 

  10. Năstăsescu, C., van Oystaeyen, F.: Graded ring theory, North–Holland, Amsterdam, 1982

Download references

Author information

Authors and Affiliations

  1. Departamento de Álgebra, Geometría y TopologÍa, Universidad de Málaga, 29071, Málaga, España

    Gonzalo Aranda Pino & Mercedes Siles Molina

Authors
  1. Gonzalo Aranda Pino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mercedes Siles Molina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gonzalo Aranda Pino.

Additional information

1) Partially supported by the MCYT and Fondos FEDER, BFM2001–1938–C02–01 and the "Plan Andaluz de Investigación y Desarrollo Tecnológico", FQM 336

The first author partially supported by an FPU grant by the MECD (AP2001–1368)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aranda Pino, G., Siles Molina, M. The Maximal Graded Left Quotient Algebra of a Graded Algebra1) . Acta Math Sinica 22, 261–270 (2006). https://doi.org/10.1007/s10114-005-0622-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0622-5

Keywords

MR (2000) Subject Classification

Search

Navigation