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- 저자 : El Maalmi, Mourad (검색결과 2 건)
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ON ALMOST QUASI-COHERENT RINGS AND ALMOST VON NEUMANN RINGS
El Alaoui, Haitham,El Maalmi, Mourad,Mouanis, Hakima Korean Mathematical Society 2022 대한수학회보 Vol.59 No.5
Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α<sub>1</sub>, …, α<sub>p</sub> and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann<sub>R</sub>(α<sup>m</sup>) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (α<sup>n</sup>, b<sup>n</sup>) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.
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El Maalmi, Mourad,Mouanis, Hakima Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
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.
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