A note on weakly n-submodules

Üregen R. N., Koç S.

Palestine Journal of Mathematics, cilt.14, sa.4, ss.1-9, 2025 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 4
  • Basım Tarihi: 2025
  • Dergi Adı: Palestine Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1-9
  • Marmara Üniversitesi Adresli: Evet

Özet

Let M be a nonzero unital module over a commutative ring R with a nonzero

identity. A proper submodule N of M is said to be a weakly n-submodule if whenever 0 ̸= am∈

N for some a ∈R and m ∈M, then a ∈ ann(M) or m ∈N. We examine the relations

between weakly n-submodules and classical submodules such as prime, weakly prime, weakly

primary and r-submodules. Also, we characterize modules over which every nonzero submodule

is secondary by using weakly n-submodules.