I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 1, PAGES 293-298
V. T. Markov
A. A. Nechaev
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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