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SYMMETRIC PROPERTY OF RINGS WITH RESPECT TO THE JACOBSON RADICAL
Calci, Tugce Pekacar,Halicioglu, Sait,Harmanci, Abdullah Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
Let R be a ring with identity and J(R) denote the Jacobson radical of R, i.e., the intersection of all maximal left ideals of R. A ring R is called J-symmetric if for any $a,b,c{\in}R$, abc = 0 implies $bac{\in}J(R)$. We prove that some results of symmetric rings can be extended to the J-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of J-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.
STRONG P-CLEANNESS OF TRIVIAL MORITA CONTEXTS
Calci, Mete B.,Halicioglu, Sait,Harmanci, Abdullah Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.