Left Nil Zero Semicommutative rings

IF 0.4 Q4 MATHEMATICS Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-29 DOI:10.5269/bspm.62926
Sanjiv Subba, T. Subedi
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引用次数: 0

Abstract

This paper introduces a class of rings called left nil zero semicommutative rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left annihilator of every nilpotent element of R is an ideal of R. It is observed that reduced rings are LNZS but not the other way around. So, this paper provides some conditions for an LNZS ring to be reduced and among other results, it is proved that R is reduced if and only if the ring of upper triangular matrices over R is LNZS. Furthermore, it is shown that the polynomial ring over an LNZS may not be LNZS and so is the case of the skew polynomial over an LNZS ring. Therefore, this paper investigates the LNZS property over the polynomial extension and skew polynomial extension of an LNZS ring with some additional conditions.
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左零半交换环
本文介绍了一类称为左零-零半交换环(LNZS环)的环,其中如果R的每个幂零元素的左零零化子是R的理想,则称环R为LNZS。因此,本文给出了一个LNZS环被约简的一些条件,并且在其他结果中,证明了R是约简的当且仅当R上的上三角矩阵环是LNZS。此外,证明了LNZS上的多项式环可能不是LNZS,LNZS环上的偏斜多项式的情况也是如此。因此,本文在一些附加条件下研究了LNZS环的多项式扩展和斜多项式扩展上的LNZS性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
140
审稿时长
25 weeks
期刊最新文献
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