ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.27, ss.83-95, 2019 (SCI İndekslerine Giren Dergi)
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
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.