TY  - JOUR
T1  - On Graded 2-n-Submodules of Graded Modules Over Graded Commutative Rings
AU  - Al- Zoubi, Khaldoun
PY  - 2024
DA  - August
Y2  - 2024
DO  - 10.55549/epstem.1523612
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 382
EP  - 389
VL  - 28
LA  - en
AB  - 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.
KW  - Graded 2-n-submodules
KW  - Graded n-submodule
KW  - Graded 2-n ideals
KW  - Graded 2-nil-ideals
CR  - 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.
UR  - https://doi.org/10.55549/epstem.1523612
L1  - https://dergipark.org.tr/en/download/article-file/4103250
ER  -