交换环的φ - (n, n) -理想

Pub Date : 2023-08-29 DOI:10.1142/s1005386723000391

Adam Anebri, N. Mahdou, Ünsal Tekir, E. Yıldız

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引用次数: 0

摘要

设[公式:见文]是一个非零单位元的交换环，且[公式:见文]是一个正整数。本文引入并研究了[公式:见文]-[公式:见文]吸收基本理想的一个新子类，称为[公式:见文]-[公式:见文]-理想。设[公式:见文]是一个函数，其中[公式:见文]表示[公式:见文]的所有理想的集合。如果[公式:见文]和[公式:见文]意味着[公式:见文]与[公式:见文]的[公式:见文]的[公式:见文]与[公式:见文]的[公式:见文]的[公式:见文]的乘积为[公式:见文]，则[公式:见文]的适当理想[公式:见文]被称为[公式:见文]-[公式:见文]-理想。除了给出[公式:见文]-[公式:见文]-理想的许多性质外，我们还使用[公式:见文]-[公式:见文]-理想的概念来表征只有有限个最小素数理想的环。

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On ϕ - ( n,N ) -ideals of Commutative Rings

Let [Formula: see text] be a commutative ring with nonzero identity and [Formula: see text] be a positive integer. In this paper, we introduce and investigate a new subclass of [Formula: see text]-[Formula: see text]-absorbing primary ideals, which are called [Formula: see text]-[Formula: see text]-ideals. Let [Formula: see text] be a function, where [Formula: see text] denotes the set of all ideals of [Formula: see text]. A proper ideal [Formula: see text] of [Formula: see text] is called a [Formula: see text]-[Formula: see text]-ideal if [Formula: see text] and [Formula: see text] imply that the product of [Formula: see text] with [Formula: see text] of [Formula: see text] is in [Formula: see text] for all [Formula: see text]. In addition to giving many properties of [Formula: see text]-[Formula: see text]-ideals, we also use the concept of [Formula: see text]-[Formula: see text]-ideals to characterize rings that have only finitely many minimal prime ideals.

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