Feckly reduced rings

Authors : Burcu UNGOR, Orhan GURGUN, Sait HALİCİOGLU, Abdullah HARMANCİ

Pages : 375-384

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Publication Date : 2015-04-01

Article Type : Research Paper

Abstract :Let R be a ring with identity and Jinsert ignore into journalissuearticles values(R); denote the Jacobson radical of R. In this paper, we introduce a new class of rings called feckly reduced rings. The ring R is called feckly reduced if R/Jinsert ignore into journalissuearticles values(R); is a reduced ring. We investigate relations between feckly reduced rings and other classes of rings. We obtain some characterizations of being a feckly reduced ring. It is proved that a ring R is feckly reduced if and only if every cyclic projective R-module has a feckly reduced endomorphism ring. Among others we show that every left Artinian ring is feckly reduced if and only if it is 2-primal, R is feckly reduced if and only if Tinsert ignore into journalissuearticles values(R, R); is feckly reduced if and only if R[x]/ < $x^{2}$ > is feckly reduced.
Keywords : reduced ring, feckly reduced ring