On (quasi-)morphic property of skew polynomial rings

Authors : Najmeh DEHGHANI

Pages : 141-156

Doi:10.24330/ieja.1102387

View : 59 | Download : 15

Publication Date : 2022-07-16

Article Type : Research Paper

Abstract :The main objective of this paper is to study insert ignore into journalissuearticles values(quasi-);morphic property of skew polynomial rings. Let $R$ be a ring, $\sigma$ be a ring homomorphism on $R$ and $n\geq 1$. We show that $R$ inherits the quasi-morphic property from $R[x;\sigma]/insert ignore into journalissuearticles values(x^{n+1});$. It is also proved that the morphic property over $R[x;\sigma]/insert ignore into journalissuearticles values(x^{n+1});$ implies that $R$ is a regular ring. Moreover, we characterize a unit-regular ring $R$ via the morphic property of $R[x;\sigma]/insert ignore into journalissuearticles values(x^{n+1});$. We also investigate the relationship between strongly regular rings and centrally morphic rings. For instance, we show that for a domain $R$, $R[x;\sigma]/insert ignore into journalissuearticles values(x^{n+1});$ is insert ignore into journalissuearticles values(left); centrally morphic if and only if $R$ is a division ring and $\sigmainsert ignore into journalissuearticles values(r);=u^{-1}ru$ for some $u\in R$. Examples which delimit and illustrate our results are provided.
Keywords : Centrally morphic ring, idempotent, morphic ring, quasi morphic ring, regular ring, strongly regular ring, unit regular ring

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