Proper classes generated by tau - closed submodules

---

Copy For Citation

DURĞUN Y., ÇOBANKAYA A.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.27, no.3, pp.83-95, 2019 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 27 Issue: 3
• Publication Date: 2019
• Doi Number: 10.2478/auom-2019-0035
• Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.83-95
• Keywords: (tau-)closed submodule, proper class, pure submodule, Goldie's torsion theory, Dickson's torsion theory, MODULES
• Çukurova University Affiliated: Yes

Abstract

The main object of this paper is to study relative homological aspects as well as further properties of tau-closed submodules. A submodule N of a module M is said to be tau-closed (or tau-pure) provided that M/N is tau-torsion-free, where tau stands for an idempotent radical. Whereas the well-known proper class Closed (Pure) of closed (pure) short exact sequences, the class tau - closed of tau-closed short exact sequences need not be a proper class. We describe the smallest proper class containing tau - Closed, through tau-closed submodules. We show that the smallest proper class is the proper classes projectively generated by the class of tau-torsion modules and coprojectively generated by the class of tau-torsion-free modules. Also, we consider the relations between the proper class and some of well-known proper classes, such as Closed; Pure.