EVENTUALLY SEMISIMPLE WEAK FI-EXTENDING MODULES

Mutlu F. T., TERCAN A., YAŞAR R.

MATHEMATICA BOHEMICA, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.21136/mb.2022.0100-21
  • Journal Name: MATHEMATICA BOHEMICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Keywords: CS-module, weak CS-module, uniform dimension, ascending chain on essen-, tial submodules, C-11-module, FI-extending, weak FI-extending, DCC, ACC
  • Hacettepe University Affiliated: Yes

Abstract

In this article, we study modules with the weak FI-extending property. We prove that if M satisfies weak FI-extending, pseudo duo, C-3 properties and M/Soc M has finite uniform dimension then M decomposes into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the weak FI-extending, pseudo duo, C-3 properties and ascending (or descending) chain condition on essential submodules then M = M-1 circle plus M-2 for some semisimple submodule M-1 and Noetherian (or Artinian, respectively) submodule M-2. Moreover, we show that a nonsingular weak CS (or weak C-11(*), or weak FI) module has a direct summand which essentially contains the socle of the module and is a CS (or C-11, or FI-extending, respectively) module.