On Right CNZ Rings with Involution

The object of this paper is to present the notion of right CNZ rings with involutions, or, in short, right *-CNZ rings which are a generalization of right *-reversible rings and an extended of CNZ property . A ring R with involution * is called right *-CNZ if for any nilpotent elements x, y є R, xy...

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Published inGeneral Letters in Mathematics Vol. 14; no. 1; pp. 17 - 24
Main Authors Ahmed, Chenar Abdul Kareem, Othman, Saman Shafiq
Format Journal Article
LanguageEnglish
Published 01.03.2024
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Summary:The object of this paper is to present the notion of right CNZ rings with involutions, or, in short, right *-CNZ rings which are a generalization of right *-reversible rings and an extended of CNZ property . A ring R with involution * is called right *-CNZ if for any nilpotent elements x, y є R, xy = 0 implies yx * = 0. Every right *-CNZ ring with unity involution is CNZ but the converse need not be true in general, even for the commutative rings. In this note, we discussed some properties right *-CNZ ring. After that we explored right *-CNZ property on the extensions and localizations of the ring R.
ISSN:2519-9269
2519-9277
DOI:10.31559/glm2024.14.1.3