交换环的弱s素数理想

Pub Date : 2021-06-01 DOI:10.2478/auom-2021-0024
F. Almahdi, E. M. Bouba, M. Tamekkante
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引用次数: 8

摘要

摘要设R是一个具有恒等的交换环,S是R的一个乘子,本文引入弱S素数理想的概念,它是弱素数理想的推广。设P是R与s不相交的理想,我们说P是R的弱s素理想,如果存在一个s∈s,使得对于所有a, b∈R,如果0≠ab∈P,则sa∈P或sb∈P,我们证明弱s素理想与弱素理想有许多类似的性质。我们还利用这一类新的理想来刻画s - noether环和s -主理想环。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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On weakly S-prime ideals of commutative rings
Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R, if 0 ≠ ab ∈ P, then sa ∈ P or sb ∈ P. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.
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