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NJ-SEMICOMMUTATIVE RINGS.
- Source :
-
Miskolc Mathematical Notes . 2023, Vol. 24 Issue 3, p1569-1579. 11p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17872405
- Volume :
- 24
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Miskolc Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 174194917
- Full Text :
- https://doi.org/10.18514/MMN.2023.4135