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- Title
NJ-SEMICOMMUTATIVE RINGS.
- Authors
SUBBA, SANJIV; SUBEDI, TIKARAM
- Abstract
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 semicom- mutative 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.
- Subjects
RIEMANNIAN geometry; INTEGRAL transforms; MATHEMATICS; INTEGRAL equations; SEMIGROUPS of operators
- Publication
Miskolc Mathematical Notes, 2023, Vol 24, Issue 3, p1569
- ISSN
1787-2405
- Publication type
Article
- DOI
10.18514/MMN.2023.4135