On delta-semiperfect modules

Hau Xuan Nguyen H. X. N., Kosan M. T., Zhou Y.

COMMUNICATIONS IN ALGEBRA, cilt.46, sa.11, ss.4965-4977, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 11
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1080/00927872.2018.1459650
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4965-4977
  • Anahtar Kelimeler: delta-Lifting module, delta-semiperfect module, projective delta-cover, semiperfect module, PERFECT RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

A submodule N of a module M is -small in M if N+XM for any proper submodule X of M with M/X singular. A projective -cover of a module M is a projective module P with an epimorphism to M whose kernel is -small in P. A module M is called -semiperfect if every factor module of M has a projective -cover. In this paper, we prove various properties, including a structure theorem and several characterizations, for -semiperfect modules. Our proofs can be adapted to generalize several results of Mares [8] and Nicholson [11] from projective semiperfect modules to arbitrary semiperfect modules.