δ-n-IDEALS OF COMMUTATIVE RINGS
MetadataShow full item record
CitationYetkin-Çelikel, E., Ulucak, G. (2022). δ-n-IDEALS OF COMMUTATIVE RINGS. Journal of Algebra and Related Topics: Cilt, 10, s. 27-42.
Let R be a commutative ring with non-zero identity, and δ: I(R) → I(R) be an ideal expansion where I(R) is the set of all ideals of R. In this paper, we introduce the concept of δ-n-ideals which is an extension of n-ideals in commutative rings. We call a proper ideal I of R a δ-n-ideal if whenever a, b ∈ R with ab ∈ I and a /∈√0, then b ∈ δ(I). For example, an ideal expansion δ1 is defined by δ1 (I) =√I. In this case, a δ1-n-ideal I is said to be a quasi n-ideal or equivalently, I is quasi n-ideal if √ I is an n-ideal. A number of characterizations and results with many supporting examples concerning this new class of ideals are given. In particular, we present some results regarding quasi n-ideals. Furthermore, we use δ-n-ideals to characterize fields and UN-rings. © 2022, University of Guilan. All rights reserved.
SourceJournal of Algebra and Related Topics
Showing items related by title, author, creator and subject.
Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1-absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1-absorbing primary ideal of R if whenever ...
Let R be a commutative ring with 1 not equal 0 and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasi-S-primary if there exists an s is an element of S such that whenever a, b is an ...
Yetkin-Çelikel, Ece (Kyungpook National University, 2021)Let R be a commutative ring with nonzero identity, I(R) the set of all idealsof R and δ: I(R) → I(R) an expansion of ideals of R. In this paper, we introduce theconcept of 2-absorbing δ-semiprimary ideals in commutative ...