We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Classical 1-Absorbing Primary Submodules.
- Authors
Yılmaz Uçar, Zeynep; Ersoy, Bayram Ali; Tekir, Ünsal; Yetkin Çelikel, Ece; Onar, Serkan
- Abstract
Over the years, prime submodules and their generalizations have played a pivotal role in commutative algebra, garnering considerable attention from numerous researchers and scholars in the field. This papers presents a generalization of 1-absorbing primary ideals, namely the classical 1-absorbing primary submodules. Let ℜ be a commutative ring and M an ℜ-module. A proper submodule K of M is called a classical 1-absorbing primary submodule of M, if x y z η ∈ K for some η ∈ M and nonunits x , y , z ∈ ℜ , then x y η ∈ K or z t η ∈ K for some t ≥ 1 . In addition to providing various characterizations of classical 1-absorbing primary submodules, we examine relationships between classical 1-absorbing primary submodules and 1-absorbing primary submodules. We also explore the properties of classical 1-absorbing primary submodules under homomorphism in factor modules, the localization modules and Cartesian product of modules. Finally, we investigate this class of submodules in amalgamated duplication of modules.
- Subjects
COMMUTATIVE algebra; COMMUTATIVE rings; NOETHERIAN rings; RESEARCH personnel; MODULES (Algebra); HOMOMORPHISMS
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 12, p1801
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12121801