Skip to main content
SpringerLink
Log in

On Identities and Varieties of Associative Algebras of Finite Type

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Varieties in which each finitely generated relatively free algebra is finitely defined are considered. A description of such varieties with identities is obtained, and a number of their structural properties are found. Bibliography: 7 titles.

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. V. T. Markov, “On generating sets of T-ideals of finitely generated free algebras,” Algebra Logica, 18, No.5, 587–598 (1979).

    Google Scholar 

  2. S. I. Kublanovsky, “On varieties of associative algebras with local conditions of finiteness,” Algebra Logica, 9, No.4, 119–174 (1997).

    Google Scholar 

  3. O. G. Kharlampovich and M. V. Sapir, “Algorithmic problems in varieties,” Internat. J. Algebra Comput., 5, Nos.4–5, 379–602 (1995); Algebra Logica, 9, No. 4, 119–174 (1997).

    Article  Google Scholar 

  4. I. N. Herstein, Noncommutative Rings, Carus Mathematical Monographs (1968).

  5. N. Jacobson, Structure of Rings, AMS (1956).

  6. S. I. Kublanovsky, “Locally finitely approximate and locally representable varieties of associative rings and algebras,” Leningrad State Pedagogical Institute, Leningrad (1982) (deposited at VINITI, No. 6143-82).

    Google Scholar 

  7. N. Bourbaki, Algebre, Chaps. IV and V.

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    S. K. Vasiliev

Authors
  1. S. K. Vasiliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 18–43.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasiliev, S.K. On Identities and Varieties of Associative Algebras of Finite Type. J Math Sci 130, 4651–4664 (2005). https://doi.org/10.1007/s10958-005-0360-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-005-0360-3

Keywords

Search

Navigation