Copy For Citation
Anebri A., Mahdou N., Tekir Ü., Yıldız E.
ALGEBRA COLLOQUIUM, vol.30, no.03, pp.481492, 2023 (SCIExpanded)

Publication Type:
Article / Article

Volume:
30
Issue:
03

Publication Date:
2023

Doi Number:
10.1142/s1005386723000391

Journal Name:
ALGEBRA COLLOQUIUM

Journal Indexes:
Science Citation Index Expanded (SCIEXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH

Page Numbers:
pp.481492

Yıldız Technical University Affiliated:
Yes
Abstract
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.