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http://dx.doi.org/10.4134/CKMS.c190140

ON g(x)-INVO CLEAN RINGS  

El Maalmi, Mourad (Faculty of Sciences Dhar El Mahraz Sidi Mohamed Ben Abdellah University)
Mouanis, Hakima (Faculty of Sciences Dhar El Mahraz Sidi Mohamed Ben Abdellah University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 455-468 More about this Journal
Abstract
An element in a ring R with identity is called invo-clean if it is the sum of an idempotent and an involution and R is called invoclean 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 ∈ C(R) and b - a ∈ 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;
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Times Cited By KSCI : 1  (Citation Analysis)
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