Modules with ADS-(pre)envelopes and ADS-(pro)covers
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.17, sa.5, 2018 (SCI-Expanded, Scopus)
- 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.