Proper classes generated by tau - closed submodules


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DURĞUN Y. , ÇOBANKAYA A.

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

  • Cilt numarası: 27 Konu: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2478/auom-2019-0035
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Sayfa Sayısı: ss.83-95

Özet

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.