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Extensions of Regular ‎Rings‎

Publish Year: 1395
Type: Journal paper
Language: English
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JR_IJIM-8-4_001

Index date: 17 January 2024

Extensions of Regular ‎Rings‎ abstract

Let R be an associative ring with identity. An element x \in R is called \mathbb{Z}G-regular (resp. strongly \mathbb{Z}G-regular) if there exist g \in G, n \in \mathbb{Z} and r \in R such that x^{ng}=x^{ng}rx^{ng} (resp. x^{ng}=x^{(n+1)g}). A ring R is called \mathbb{Z}G-regular (resp. strongly \mathbb{Z}G-regular) if every element of R is \mathbb{Z}G-regular (resp. strongly \mathbb{Z}G-regular). In this paper, we characterize \mathbb{Z}G-regular (resp. strongly \mathbb{Z}G-regular) rings. Furthermore, this paper includes a brief discussion of \mathbb{Z}G-regularity in group ‎rings.‎

Extensions of Regular ‎Rings‎ Keywords:

Extensions of Regular ‎Rings‎ authors

SH. A. Safari ‎Sabet‎

Department of ‎Mathematics,‎ Central Tehran Branch, Islamic Azad University, Tehran, ‎Iran‎

M. Farmani

Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, ‎Iran