Special regular clean rings

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Gogoi Saurav Jyoti; Saikia Helen K.

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Journal Paper

Paper Information

Journal: Algebraic structures and their applications Year:2025 | Volume:12 | Issue:1 Page(s): 23-32

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Information Journal Paper

Title

Special regular clean rings

Author(s)

Gogoi Saurav Jyoti | Saikia Helen K. | Issue Writer Certificate

Keywords

r-clean ring

Special clean ring

Special rclean ring

Twisted power series ring

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 ∈ R and unit u ∈ 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, σ]] is a special regular clean ring. We also study various characterizations of special clean and special regular clean rings.

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