Abstract
References
- Al-Zoubi, K. (2024). On graded 2-n-submodules of graded modules over graded commutative rings. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 382-389.
Abstract
In this article, all rings are commutative with a nonzero identity. Let G be a group with identity e, R be a G-graded commutative ring, and M be a graded R-module. In 2019, the concept of graded n-ideals was introduced and studied by Al-Zoubi, Al-Turman, and Celikel. A proper graded ideal I of R is said to be a graded n-ideal of R if whenever r,s∈h(R) with rs∈I and r∉Gr(0), then s∈I. In 2023, the notion of graded n-ideals was recently extended to graded n-submodules by Al-Azaizeh and Al-Zoubi. A proper graded submodule N of a graded R-module M is said to be a graded n-submodule if whenever t∈h(R), m∈h(R) with tm∈N and t∉Gr(Ann_R (M)), then m∈N. In this study, we introduce the concept of graded 2-n-submodules of graded modules over graded commutative rings generalizing the concept of graded n-submodules. We investigate some characterizations of graded 2-n-submodules and investigate the behavior of this structure under graded homomorphism and graded localization. A proper graded submodule U of M is said to be a graded 2-n-submodule if whenever r,s∈h(R), m∈(M) and rsm∈U, then rs∈Gr(Ann_R (M)) or rm∈U or tm∈U.
References
- Al-Zoubi, K. (2024). On graded 2-n-submodules of graded modules over graded commutative rings. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 382-389.
Details
| Primary Language | English |
|---|---|
| Subjects | Software Engineering (Other) |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | July 29, 2024 |
| Publication Date | August 1, 2024 |
| Submission Date | February 13, 2024 |
| Acceptance Date | April 10, 2024 |
| Published in Issue | Year 2024Volume: 28 |
