The pi-extending Property via Singular Quotient Submodules

KARA ŞEN Y., TERCAN A.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.59, no.3, pp.391-401, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.5666/kmj.2019.59.3.391
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.391-401
  • Hacettepe University Affiliated: Yes

Abstract

A module is said to be pi-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this article, we focus on the class of modules having the pi-extending property by looking at the singularity of quotient submodules. By doing so, we provide counterexamples, using hypersurfaces in projective spaces over complex numbers, to show that being generalized pi-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized pi-extending modules are generalized pi-extending.