FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

Radicals of semiperfect rings related to idempotents

V. T. Markov
A. A. Nechaev

Abstract

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For a semiperfect ring $A$ we prove the existence of the minimal ideal $$M(A) (modular radical) such that the quotient ring $A/$M(A) has the identity element, and of the minimal ideal $$W(A) (Wedderburn radical) such that the quotient ring $A/$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