Skip to main content
Log in

On T-spaces and related concepts and results

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

Abstract

This paper is a brief survey of the T-space concept and related results. A connection between T-spaces and so-called varieties of pairs, analogous to the connection between T-ideals and varieties of algebras, is established. The concepts of A-equivalency and T-equivalency are introduced, after which some applications are considered.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. V. Aladova, A. V. Grishin, and E. A. Kireeva, “T-spaces. Background, applications and latest results,” Chebyshevskii Sb., 5, No. 4 (12), 39–57 (2004).

    MATH  MathSciNet  Google Scholar 

  2. A. V. Grishin, “On the finite basis property for systems of generalized polynomials,” Math. USSR Izv., 37, No. 2, 243–272 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  3. A. V. Grishin, “On the finite basis property of abstract T-spaces,” Fundam. Prikl. Mat., 1, No. 3, 669–700 (1995).

    MATH  MathSciNet  Google Scholar 

  4. A. V. Grishin, “Examples of T-spaces and T-ideals over a field of characteristic 2 without the finite basis property,” Fundam. Prikl. Mat., 5, No. 1, 101–118 (1999).

    MATH  MathSciNet  Google Scholar 

  5. A. V. Grishin and V. V. Shchigolev, “On T-spaces and their applications,” J. Math. Sci., 134, No. 1, 1799–1878 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. R. Kemer, “Finite basability of identities of associative algebras,” Algebra Logika, 26, No. 5, 597–641 (1987).

    MATH  MathSciNet  Google Scholar 

  7. S. V. Okhitin, “Central polynomials of an algebra of second-order matrices,” Moscow Univ. Math. Bull., 43, No. 4, 49–51 (1988).

    MATH  MathSciNet  Google Scholar 

  8. Yu. P. Razmyslov, “A certain problem of Kaplansky,” Izv. Akad. Nauk SSSR, Ser. Mat., 37, No. 3, 4834–501 (1973).

    MathSciNet  Google Scholar 

  9. Yu. P. Razmyslov, “On the finite basis property of identities of matrix algebra of second order over a field of characteristic zero,” Algebra Logika, 12, No. 1, 83–113 (1973).

    MathSciNet  Google Scholar 

  10. V. V. Shchigolev, “Examples of T-spaces with an infinite basis,” Mat. Sb., 191, No. 3, 459–476 (2000).

    Article  MathSciNet  Google Scholar 

  11. V. V. Shchigolev, “Finite basis property of T-spaces over fields of characteristic zero,” Izv. Ross. Akad. Nauk, Ser. Mat., 65, No. 5, 1041–1071 (2001).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Grishin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 5, pp. 77–84, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grishin, A.V. On T-spaces and related concepts and results. J Math Sci 163, 677–681 (2009). https://doi.org/10.1007/s10958-009-9703-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-009-9703-9

Keywords

Navigation