ON SUBINJECTIVITY DOMAINS OF PURE-INJECTIVE MODULES
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.51, sa.4, ss.1227-1238, 2021 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 51 Sayı: 4
- Basım Tarihi: 2021
- Doi Numarası: 10.1216/rmj.2021.51.1227
- Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.1227-1238
- Anahtar Kelimeler: pure-injective module, subinjective domain, pi-indigent module, absolutely pure module, ALTERNATIVE PERSPECTIVE, RINGS, PURITY
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Çukurova Üniversitesi Adresli: Evet
Özet
A pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest possible, namely, consisting of exactly the absolutely pure modules. A module M is called subinjective relative to a module N if for every extension K of N, every homomorphism N -> M can be extended to a homomorphism K -> M. The subinjectivity domain of the module M is defined to be the class of modules N such that M is N-subinjective. Basic properties of the subinjectivity domains of pure-injective modules and of pi-indigent modules are studied. The structure of a ring over which every simple, uniform, or indecomposable pure-injective module is injective or subinjective relative only to the smallest possible family of modules is investigated.