Öz
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
Graded 2-n-submodules Graded n-submodule Graded 2-n ideals Graded 2-nil-ideals
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Yazılım Mühendisliği (Diğer) |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 29 Temmuz 2024 |
| Yayımlanma Tarihi | 1 Ağustos 2024 |
| Gönderilme Tarihi | 13 Şubat 2024 |
| Kabul Tarihi | 10 Nisan 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 28 |
