Version 1
: Received: 26 February 2024 / Approved: 26 February 2024 / Online: 26 February 2024 (15:33:56 CET)
How to cite:
Yetkin Celikel, E.; Khashan, H. (m, n)-Closed Submodules of Modules over Commutative Rings. Preprints2024, 2024021484. https://doi.org/10.20944/preprints202402.1484.v1
Yetkin Celikel, E.; Khashan, H. (m, n)-Closed Submodules of Modules over Commutative Rings. Preprints 2024, 2024021484. https://doi.org/10.20944/preprints202402.1484.v1
Yetkin Celikel, E.; Khashan, H. (m, n)-Closed Submodules of Modules over Commutative Rings. Preprints2024, 2024021484. https://doi.org/10.20944/preprints202402.1484.v1
APA Style
Yetkin Celikel, E., & Khashan, H. (2024). (m, n)-Closed Submodules of Modules over Commutative Rings. Preprints. https://doi.org/10.20944/preprints202402.1484.v1
Chicago/Turabian Style
Yetkin Celikel, E. and Hani Khashan. 2024 "(m, n)-Closed Submodules of Modules over Commutative Rings" Preprints. https://doi.org/10.20944/preprints202402.1484.v1
Abstract
Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈N implies rⁿ∈(N:_{R}M) or b∈N. This class of submodules lies properly between the classes of prime and primary submodules. Many characterizations, properties and supporting examples concerning this class of submodules are provided. The notion of (m,n)-modules is introduced and characterized. Furhermore, the (m,n)-closed avoidance theorem is proved. Finally, the (m,n)-closed submodules in amalgamated modules are studied.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
