Modules in which semisimple fully invariant submodules are essential in summands

YAŞAR R.

Turkish Journal of Mathematics, cilt.43, sa.5, ss.2327-2336, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1906-36
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2327-2336
  • Anahtar Kelimeler: C11-module, Extending module, FI -extending, Fully invariant, Socle of a module, Weak CS -module
  • Ankara Üniversitesi Adresli: Hayır

Özet

One of the useful generalization of extending notion is FI -extending property. A module is called FI - extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak FI - extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak FI -extending. We obtain that FI -extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak FI -extending modules.