Generalized Reflexive Structures Properties of Crossed Products Type

Author:

Ali Eltiyeb

Abstract

      Let $R$ be a ring and $M$ be a monoid with a twisting map $f : M \times M \rightarrow U(R)$ and an action map $\omega : M \rightarrow Aut(R)$. The objective of our work is to extend the reflexive properties of rings by focusing on the crossed product $R \ast M$ over $R$. In order to achieve this, we introduce and examine the concept of strongly $CM$-reflexive rings. Although a monoid $M$ and any ring $R$ with an idempotent are not strongly $CM$-reflexive in general, we prove that $R$ is strongly $CM$-reflexive under some additional conditions. Moreover, we prove that if $R$ is a left $p.q.$-Baer (semiprime, left $APP$-ring, respectively), then $R$ is strongly $CM$-reflexive. Additionally, for a right Ore ring $R$ with a classical right quotient ring $Q$, we prove $R$ is strongly $CM$-reflexive if and only if $Q$ is strongly $CM$-reflexive. Finally, we discuss some relevant results on crossed products.

Publisher

New York Business Global LLC

Subject

Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Some Results of Malcev-Neumann Rings;International Journal of Analysis and Applications;2024-02-27

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3