Skip to main content

On Sums of Radical and Regular Rings

Abstract

We find conditions which ensure that a ring is adjoint regular provided that it is a sum of a radical subring with an adjoint regular subring. We also provide a criterion of adjoint regularity for a ring which is a sum of its radical and a regular subring.

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

REFERENCES

  1. 1.

    V. A. Andranukievich and Yu. M. Ryabukhin, Radicals of Algebras and Structure Theory [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. 2.

    W. E. Clark, “Generalized radical rings,” Canad. J. Math., 20, No.1, 88–94 (1968).

    Google Scholar 

  3. 3.

    Du Xiankun, “The structure of generalized radical rings,” Northeastern Math. J., 4, No.1, 101–114 (1988).

    Google Scholar 

  4. 4.

    Du Xiankun, “The rings with regular adjoint semigroups,” Northeastern Math. J., 4, No.4, 483–488 (1988).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 71–75, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Volkov, M.V., Tanana, G.V. On Sums of Radical and Regular Rings. J Math Sci 128, 3378–3380 (2005). https://doi.org/10.1007/s10958-005-0275-z

Download citation

Keywords

  • Regular Ring