F-supplemented modules

Creative Commons License

Ozdemir S.

ALGEBRA & DISCRETE MATHEMATICS, cilt.30, sa.1, ss.83-96, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.12958/adm1185
  • Dergi Adı: ALGEBRA & DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.83-96
  • Anahtar Kelimeler: F-supplement and F-small submodules, F-supplemented, F-local and F-hollow modules
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let R be a ring, let M be a left R-module, and let U, V, F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F subset of X subset of M such that U + X = M, or equivalently, F subset of V, U +V = M and U boolean AND V is F-small in V. If every submodule of M has an F-supplement, then we call M an F-supplemented module. In this paper, we introduce and investigate F-supplement submodules and (amply) F-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) F-supplemented modules in terms of their certain submodules.