ON g(x)-INVO CLEAN RINGS
Commun. Korean Math. Soc.
Published online January 29, 2020
Mourad EL Maalmi and Hakima Mouanis
University of Sidi Mohammed Ben Abdellah, Faculty of Sciences Dhar el Mahraz
Abstract : An element in a ring $R$ with identity is called invo-clean if it is the sum of an idempotent and an involution, $R$ is called invo-clean if every element of $R$ is invo-clean. Let $C(R)$ be the center of a ring $R$ and $g(x)$ be a fixed polynomial in $C(R)[x]$. We introduce the new notion of $g(x)$-invo clean. $R$ is called $g(x)$-invo if every element in $R$ is a sum of an involution and a root of $g(x)$. In this paper, we investigate many properties and examples of $g(x)$-invo clean rings. Moreover, we characterize invo-clean as $g(x)$-invo clean rings where $g(x)=(x-a)(x-b)$, $a,b\in C(R)$ and $b-a\in Inv(R)$. Finally, some classes of $g(x)$-invo clean rings are discussed.
Keywords : Invo-clean ring, $g(x)$-invo clean ring, unitly invo-clean ring, amalgamated algebra.
MSC numbers : 13A99, 16D60, 16U99
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