Copy For Citation
Anebri A., Mahdou N., Tekir Ü., Yıldız E.
ALGEBRA COLLOQUIUM, vol.30, no.03, pp.481-492, 2023 (SCI-Expanded)
-
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 (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
-
Page Numbers:
pp.481-492
-
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.