Generalized weakly central reduced rings

Authors: YING ZHOU, JUNCHAO WEI

Abstract: A ring $R$ is called $GWCN$ if $x^2y^2=xy^2x$ for all $x\in N(R)$ and $y\in R$, which is a proper generalization of reduced rings and $CN$ rings. We study the sufficient conditions for $GWCN$ rings to be reduced and $CN$. We first discuss many properties of $GWCN$ rings. Next, we give some interesting characterizations of left min-abel rings. Finally, with the help of exchange $GWCN$ rings, we obtain some characterizations of strongly regular rings.

Keywords: $GWCN$ rings, $CN$ rings, reduced rings, strongly regular rings, left min-abel rings, exchange rings, clean rings

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