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IMI/Publicaţii/BASM/Ediţii/BASM n.1 (65), 2011/

Serial rings and their generalizations

Authors: Vladimir Kirichenko, Makar Plakhotnyk

Abstract

We give a survey of results on the theory of semiprime semidistributive rings, in particular, serial rings. Besides this we prove that a serial ring is Artinian if and only if some power of its Jacobson radical is zero. Also we prove that a serial ring is Noetherian if and only if the intersection of all powers of Jacobson radical is zero. These two theorems hold for semiperfect semidistributive rings.

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