Skip to main content
SpringerLink
Log in

The group K 0 of a generalized matrix ring

  • Published:
Algebra and Logic Aims and scope

We deal with a group K 0 of some category of modules over a generalized matrix ring (of order 2). The results obtained are applied to compute the group K 0 for the generalized matrix ring itself.

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. P. A. Krylov, “Isomorphism of generalized matrix rings,” Algebra Logika, 47, No. 4, 456–463 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  2. P. A. Krylov, “Injective modules over formal matrix rings,” Sib. Mat. Zh., 51, No. 1, 90–97 (2010).

    Article  Google Scholar 

  3. P. A. Krylov and A. A. Tuganbaev, “Modules over formal matrix rings,” Fund. Prikl. Mat., 15, No. 8, 145–211 (2009).

    Google Scholar 

  4. H. Chen, “Stable ranges for Morita contexts,” Southeast Asian Bull. Math., 25, No. 2, 209–216 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Chen, “Morita contexts with many units,” Comm. Alg., 30, No. 3, 1499–1512 (2002).

    Article  MATH  Google Scholar 

  6. A. Haghany and K. Varadarajan, “Study of modules over formal triangular matrix rings,” J. Pure Appl. Alg., 147, No. 1, 41–58 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Loustaunau and J. Shapiro, “Morita contexts,” in Non-Commutative Ring Theory, Proc. Conf., Athens/OH (USA), 1989, Lect. Notes Math., 1448, Springer-Verlag, Berlin, (1990), pp. 80–92.

  8. R. Khazal, S. Dascalescu, and L. van Wyk, “Isomorphism of generalized triangular matrix rings and recovery of tiles,” Int. J. Math. Math. Sci., No. 9, 533–538 (2003).

  9. D. Sheiham, “Universal localization of triangular matrix rings,” Proc. Am. Math. Soc., 134, No. 12, 3465–3474 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  10. Z. Xiao and F. Wei, “Commuting mappings of generalized matrix algebras,” Lin. Alg. Appl., 433, Nos. 11/12, 2178–2197 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Li and F. Wei, “Semi-centralizing maps of generalized matrix algebras,” Lin. Alg. Appl., 436, No. 5, 1122–1153 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  12. G. Tang and Y. Zhou, “Strong cleanness of generalized matrix rings over a local ring,” Lin. Alg. Appl., 437, No. 10, 2546–2559 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  13. R. K. Dennis and S. C. Geller, “K i of upper triangular matrix rings,” Proc. Am. Math. Soc., 56, 73–78 (1976).

    MathSciNet  MATH  Google Scholar 

  14. P. A.Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups, Algebras Appl., 2, Kluwer, Boston, MA (2003).

  15. D. M. Arnold, Finite Rank Torsion-Free Abelian Groups and Rings, Lect. Notes Math., 931, Springer-Verlag, Berlin (1982).

  16. H. Bass, Algebraic K-Theory, Benjamin, New York (1968).

    MATH  Google Scholar 

  17. J. Milnor, Introduction to Algebraic K-Theory, Ann. Math. Stud., 72, Princeton Univ. Press, Princeton (1971).

  18. J. Rosenberg, Algebraic K-Theory and Its Applications, Grad. Texts Math., 147, Springer-Verlag, New York (1994).

  19. V. Srinivas, Algebraic K-Theory, Prog. Math., 90, Birkhäuser, Boston, MA (1991).

  20. C. Feys, Algebra: Rings, Modules and Categories, Vols. 1, 2, Springer, Berlin (1973).

Download references

Author information

Authors and Affiliations

  1. Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia

    P. A. Krylov

Authors
  1. P. A. Krylov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. A. Krylov.

Additional information

Translated from Algebra i Logika, Vol. 52, No. 3, pp. 370-385, May-June, 2013.

*Supported by the Russian Ministry of Education and Science, gov. contract No. 14.B37.21.0354.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krylov, P.A. The group K 0 of a generalized matrix ring. Algebra Logic 52, 250–261 (2013). https://doi.org/10.1007/s10469-013-9238-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-013-9238-5

Keywords

Search

Navigation