FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 293-298

V. T. Markov

A. A. Nechaev

Abstract

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For a semiperfect ring
```$A$ we prove the existence of the minimal ideal
$\mathcal M(A)$ (modular radical) such that the quotient ring
$A/\mathcal M(A)$ has the identity element, and of the minimal ideal
$\mathcal W(A)$ (Wedderburn radical) such that the quotient ring
$A/\mathcal W(A)$ is decomposable into a direct sum of matrix rings
over local rings. A simple criterion of such decomposability
is given for left Noetherian semiperfect rings and left perfect rings.

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Last modified: April 11, 2000