Classical 1-Absorbing Primary Submodules

Zeynep Yılmaz Uçar, Bayram Ali Ersoy, Ünsal Tekir, Ece Yetkin Çelikel () and Serkan Onar
Additional contact information
Zeynep Yılmaz Uçar: Department of Mathematics, Yildiz Technical University, Istanbul 34220, Türkiye
Bayram Ali Ersoy: Department of Mathematics, Yildiz Technical University, Istanbul 34220, Türkiye
Ünsal Tekir: Department of Mathematics, Marmara University, Istanbul 34722, Türkiye
Ece Yetkin Çelikel: Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep 27010, Türkiye
Serkan Onar: Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34220, Türkiye

Mathematics, 2024, vol. 12, issue 12, 1-13

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.

Keywords: primary submodule; 1-absorbing primary submodule; classical primary submodule; classical 1-absorbing primary submodule (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/12/1801/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/12/1801/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:12:p:1801-:d:1411966

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().