The pi-extending Property via Singular Quotient Submodules

KARA ŞEN Y., TERCAN A.

KYUNGPOOK MATHEMATICAL JOURNAL, cilt.59, sa.3, ss.391-401, 2019 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.5666/kmj.2019.59.3.391
  • Dergi Adı: KYUNGPOOK MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.391-401
  • Hacettepe Üniversitesi Adresli: Evet

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 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.