Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 5
Generalized weakly central reduced rings
- Sayfa
- 604–617
- DOI
- —
Özet
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.
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.