On weakly classical 1-absorbing prime submodules

Creative Commons License

Uçar Z., Ersoy B. A., Tekir Ü., Koç S., Onar S.

OPEN MATHEMATICS, cilt.2025, sa.23(1), ss.1-14, 2025 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 23(1)
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/math-2025-0215
  • Dergi Adı: OPEN MATHEMATICS
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1-14
  • Marmara Üniversitesi Adresli: Evet

Özet

In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital module M over a commutative ring R having a nonzero identity. A proper submodule N of M is said to be a weakly classical 1-absorbing prime submodule, if for each m ∈ M and nonunits a, b, c ∈ R, 0 ≠ abcm ∈ N implies that abm ∈ N or cm ∈ N. We give various examples and properties of weakly classical 1-absorbing prime submodules. Also, we investiage the weakly classical 1-absorbing prime submodules of tensor product F ⊗ M of a (faithfully) flat R-module F and any R-module M. Also, we prove that if every proper submodule of an R-module M is weakly classical 1-absorbing prime, then Jac(R) 3M = 0. In terms of this result, we characterize modules over local rings in which every proper submodule is weakly classical 1-absorbing prime.