Skip to main content

Hidden matrix semirings

Abstract

Criteria analogous to Robson’s and Fuchs’ are given for a semiring to be isomorphic to a full matrix semiring. The necessity of additional conditions (compared with the case of rings) is investigated.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    A. W. Chatters, “Representation of tiled matrix rings as full matrix rings,” Math. Proc. Cambridge Philos. Soc., 105, 67–72 (1989).

    MATH  MathSciNet  Article  Google Scholar 

  2. 2.

    P. R. Fuchs, “A characterization result for matrix rings,” Bull. Austral. Math. Soc., 43, 265–267 (1991).

    MATH  MathSciNet  Article  Google Scholar 

  3. 3.

    J. S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science, Pitman (1991).

  4. 4.

    A. V. Mikhalev, “Isomorphisms and antiisomorphisms of endomorphism rings of modules,” in: First International Tainan-Moscow Algebra Workshop, Walter de Gruyter, Berlin—New York (1996), pp. 70–122.

    Google Scholar 

  5. 5.

    J. C. Robson, “Recognition of matrix rings,” Comm. Algebra, 19, No. 7, 2113–2124 (1991).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 13–19, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bogdanov, I.I. Hidden matrix semirings. J Math Sci 135, 3276–3280 (2006). https://doi.org/10.1007/s10958-006-0157-z

Download citation

Keywords

  • Additional Condition
  • Full Matrix
  • Matrix Semiring
  • Hide Matrix