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Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings
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作者 Eltiyeb Ali 《Advances in Pure Mathematics》 2022年第11期676-692,共17页
Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized p... Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory. 展开更多
关键词 left app-ring Generalized Power Series Reflexive ring Nil Generalized Power Series Reflexive ring S-Quasi Armendariz ring Semiprime ring Semicommutative ring
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弱M-拟Armendariz环的性质及等价刻画 被引量:2
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作者 丁婷婷 吴俊 张培雨 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2014年第1期17-22,共6页
利用某些矩阵环的特殊性质,得到了环R是弱M-拟Armendariz环当且仅当环Tn(R)是弱M-拟Armendariz环.
关键词 弱M-拟Armendariz环 M-拟Armendariz环 拟弱Armendariz环 app-环 半交换环
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