The pi-extending Property via Singular Quotient Submodules
KYUNGPOOK MATHEMATICAL JOURNAL, cilt.59, sa.3, ss.391-401, 2019 (ESCI, Scopus)
- 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
- Bursa Uludağ 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.