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.
ZHOU, YING and WEI, JUNCHAO
"Generalized weakly central reduced rings,"
Turkish Journal of Mathematics: Vol. 39:
5, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss5/2