SOME CHARACTERIZATIONS OF ARTINIAN RINGS

Authors : H Khabazian

Pages : 1-9

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Publication Date : 2011-06-01

Article Type : Research Paper

Abstract :In this paper, we investigate rings in which the prime radical is an annihilator and present a characterization of Artinian rings satisfying this property. We also study rings in which the singular ideal and the prime radical coincide. Finally we show that Artinian rings are the direct product of a semiprime ring and a semiprime-free ring insert ignore into journalissuearticles values(ring in which every nonzero ideal contains a nonzero nilpotent ideal); and present a result on quasi-Baer Artinian rings.
Keywords : prime, semiprime, semiprime free, rAI semiprime, Artinian, quasiBaer, QF, essential, annihilator