EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 102[116], pp. 195–202 (2017)

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Topologically boolean and g(x)-clean rings

Angelina Yan Mui Chin, Kiat Tat Qua

Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia; Department of Mathematical and Actuarial Sciences, University Tunku Abdul Rahman, Kajang, Selangor, Malaysia

Abstract: Let R be a ring with identity and let g(x) be a polynomial in Z(R)[x] where Z(R) denotes the center of R. An element rR is called g(x)-clean if r=u+s for some u,sR such that u is a unit and g(s)=0. The ring R is g(x)-clean if every element of R is g(x)-clean. We consider g(x)=x(x-c) where c is a unit in R such that every root of g(x) is central in R. We show, via set-theoretic topology, that among conditions equivalent to R being g(x)-clean, is that R is right (left) c-topologically boolean.

Keywords: g(x)-clean, n-clean, topologically boolean

Classification (MSC2000): 16U99

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Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.

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