Weak FI-extending Modules with ACC or DCC on Essential Submodules

TERCAN A., YAŞAR R.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.61, no.2, pp.239-248, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.5666/kmj.2021.61.2.239
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.239-248
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we study modules with the WFI+-extending property. We prove that if M satisfies the WFI+-extending, pseudo duo properties and M=(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the WFI+ extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M-1 circle plus M-2 for some semisimple submodule M-1 and Noetherian (respectively, Artinian) submodule M-2. Moreover, we show that if M is a WFI-extending module with pseudo duo, C-2 and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.