On NCS modules and rings

KARABACAK F., KOŞAN M. T., Quynh T. C., Tai D. D., Tasdemir O.

COMMUNICATIONS IN ALGEBRA, vol.48, no.12, pp.5236-5246, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 48 Issue: 12
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1784910
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5236-5246
  • Keywords: Complement submodule, small submodule, CS module, NCS module, ADS-module, QF-ring, p-injective ring, GP-injective ring
  • Anadolu University Affiliated: Yes

Abstract

We give some conditions as to when a (finite) direct sum of NCS modules (if no non-zero complement submodule is small) is again NCS, and also provide various conditions to be sufficient for a submodule of an NCS module to be NCS. Some comparisons between QF-rings, GP-injective rings, AGP-rings and NCS rings are investigated.