Generalized Reflexive Structures Properties of Crossed Products Type


  • Eltiyeb Ali University of Khartoum



Cross Product., $CM$-quasi Armendariz ring, strongly $CM$-reflexive ring


      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.






Nonlinear Analysis

How to Cite

Generalized Reflexive Structures Properties of Crossed Products Type. (2023). European Journal of Pure and Applied Mathematics, 16(4), 2156-2168.

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