PI-extending modules via nontrivial complex bundles and Abelian endomorphism rings

KARA ŞEN Y., TERCAN A., YAŞAR R.

Bulletin of the Iranian Mathematical Society, cilt.43, sa.1, ss.121-129, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 1
  • Basım Tarihi: 2017
  • Dergi Adı: Bulletin of the Iranian Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.121-129
  • Anahtar Kelimeler: Exchange property, Extending module, Projective invariant, Tangent bundle
  • Ankara Üniversitesi Adresli: Hayır

Özet

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.