NJ-semicommutative Rings
Sanjiv Subba, Tikaram Subedi · Miskolc mathematical notes/Mathematical notes · 2023
We call a ring R NJ-semicommutative if wh ∈ N(R) implies wRh ⊆ J(R) for any w, h ∈ 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 NJsemicommutative ring R for which R/J(R) is reduced.We also study some extensions of NJsemicommutative rings wherein, among other results, we prove that the polynomial ring over an NJ-semicommutative ring need not be NJ-semicommutative.