Pointwise Semicommutative Rings
Rings and Algebras
2022-06-06 v1
Abstract
We call a ring R pointwise semicommutative if for any element a in R either l(a) or r(a) is an ideal of R. A class of pointwise semicommutative rings is a strict generalization of semicommutative rings. Since reduced rings are pointwise semicommutative, this paper studies sufficient conditions for pointwise semicommutative rings to be reduced. For a pointwise semicommutative ring R, R is strongly regular if and only if R left SF ; R is exchange if and only if R is clean; if R is semiperiodic then R/J(R) is commutative.
Cite
@article{arxiv.2206.01464,
title = {Pointwise Semicommutative Rings},
author = {Sanjiv Subba and Tikaram Subedi and A. M. Buhphang},
journal= {arXiv preprint arXiv:2206.01464},
year = {2022}
}