On the inheritance of the strongly π-extending property

Kara Y. , TERCAN A.

Communications in Algebra, vol.45, no.8, pp.3627-3635, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1243245
  • Title of Journal : Communications in Algebra
  • Page Numbers: pp.3627-3635
  • Keywords: Endomorphsim ring, pi-extending module, generalized triangular matrix ring, projection invariant, MODULES, SUBMODULES, SUMMANDS, RINGS

Abstract

© 2017 Taylor & Francis.In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.