The pi-extending Property via Singular Quotient Submodules


KARA ŞEN Y. , TERCAN A.

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

  • Publication Type: Article / Article
  • Volume: 59 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.5666/kmj.2019.59.3.391
  • Title of Journal : KYUNGPOOK MATHEMATICAL JOURNAL
  • Page Numbers: pp.391-401

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.