Extensions of Regular Rings
Publish Year: 1395
Type: Journal paper
Language: English
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Document National Code:
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.
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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