Special regular clean rings

Document Type : Research Paper

Authors

Department of Mathematics, Gauhati University, Jalukbari, Guwahati, India.

Abstract

In this paper we introduce the concepts of special regular clean elements and regular clean decomposition in a ring R. These concepts lead us to the notion of special regular clean ring. We prove that for a special regular clean element $a=e+r \in R$ and unit $u\in R$ then $au$ is a special regular clean if $u$ is an inner inverse of $e$. We establish that an abelian ring $R$ is a special regular clean ring if and only if the twisted power series ring $R[[x,\sigma]]$ is a special regular clean ring. We also study various characterizations of special clean and special regular clean rings.

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References

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Algebraic Structures and Their Applications

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Available Online from 28 June 2024

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