On tau-Extending Modules

Ceken S., ALKAN M.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.9, sa.1, ss.129-142, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1007/s00009-010-0096-2
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.129-142
  • Anahtar Kelimeler: tau-large submodule, tau-closed submodule, extending module, tau-complemented module, tau-CS module
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of tau-large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with the familiar concepts of tau-closed, tau-complement submodules and the other generalization of extending modules (tau-complemented, tau-CS, s-tau-CS modules). We are also interested in determining when a tau-divisible module is tau-extending. For a tau-extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that M = tau(M) circle plus K and K is tau (M)-injective. We also treat when a direct sum of tau-extending modules is tau-extending.