Modules with ADS-(pre)envelopes and ADS-(pro)covers

Truong Cong Quynh T. C. Q., Kosan M. T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.17, sa.5, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s0219498818500962
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: ADS module, (pre)envelope, (pre)cover, Noetherian ring, V-ring, ADS MODULES, RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

This paper focusses on the question of when modules have ADS- preenvelopes and covers. For a ring R, it is proved that every ADS module over R is injective if and only if every right R-module has an ADS-(pre)envelope (an ADS-(pre)cover). In this paper, we also introduce a generalization of ADS modules stated in terms of their invariance under certain automorphisms of their envelopes.