Modules in which semisimple fully invariant submodules are essential in summands

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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
  • Hacettepe Üniversitesi Adresli: Evet

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.