• Title/Summary/Keyword: invo-clean rings

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ON g(x)-INVO CLEAN RINGS

  • El Maalmi, Mourad;Mouanis, Hakima
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.455-468
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    • 2020
  • 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.

INVO-CLEAN UNITAL RINGS

  • Danchev, Peter V.
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.19-27
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    • 2017
  • We define and completely describe the structure of invo-clean rings having identity. We show that these rings are clean but not (weakly) nil-clean and thus they possess independent properties than these obtained by Diesl in [7] and by Breaz-Danchev-Zhou in [2].