t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS -اول و تجزیه آن هاtزیرمدول های

Moghaderi J., TERCAN A. E.

Journal of Algebraic Systems, cilt.14, sa.2, ss.369-381, 2026 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.22044/jas.2024.14373.1822
  • Dergi Adı: Journal of Algebraic Systems
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.369-381
  • Anahtar Kelimeler: Primary submodule, Prime submodule, t-Prime submodule
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with identity. For t ∈ N, a proper submodule N of an R-module M is called a t-prime submodule if rm ∈ N (r ∈ R, m ∈ M), then m ∈ N or rt ∈ (N :R M). We obtain some other characterizations of t-prime submodules. Also, by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples to illustrate our results.