PI-EXTENDING MODULES VIA NONTRIVIAL COMPLEX BUNDLES AND ABELIAN ENDOMORPHISM RINGS

Kara Y., Tercan A., Yasar R.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.43, no.1, pp.121-129, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2017
  • Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.121-129
  • Keywords: Extending module, projective invariant, tangent bundle, exchange property, DIRECT-SUMMANDS, SUBMODULES, RANK
  • 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 paper, we focus on direct summands and indecomposable decompositions of PI-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper surfaces in projective spaces over complex numbers and obtain results when the PI-extending property is inherited by direct summands. Moreover, we show that under some module theoretical conditions PI-extending modules with Abelian endomorphism rings have indecomposable decompositions. Finally, under suitable hypotheses, we apply our former results to obtain that the finite exchange property implies the full exchange property.