MMN-4135

We call a ring $R$ NJ-semicommutative if $wh\in N(R)$ implies $wRh\subseteq J(R)$ for any $w,h\in R$. The class of NJ-semicommutative rings is large enough that it contains semicommutative rings, left (right) quasi-duo rings, J-clean rings, and J-quasipolar rings. We provide some conditions for NJ-semicommutative rings to be reduced. We also observe that if $R/J(R)$ is reduced, then $R$ is NJ-semicommutative, and therefore we provide some conditions for NJ-semicommutative ring $R$ for which $R/J(R)$ is reduced. We also study some extensions of NJ-semicommutative rings wherein, among other results, we prove that the polynomial ring over an NJ-semicommutative ring need not be NJ-semicommutative.

Vol. 24 (2023), No. 3, pp. 1569-1579

DOI: 10.18514/MMN.2023.4135

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