CONEAT SUBMODULES AND CONEAT-FLAT MODULES
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.51, sa.6, ss.1305-1319, 2014 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 51 Sayı: 6
- Basım Tarihi: 2014
- Doi Numarası: 10.4134/jkms.2014.51.6.1305
- Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1305-1319
- Anahtar Kelimeler: neat submodule, coclosed submodule, coneat submodule, coneat-flat module, absolutely neat module
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Çukurova Üniversitesi Adresli: Hayır
Özet
A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism N -> S can be extended to a homomorphism M -> S. M is called coneat-flat if the kernel of any epimorphism Y -> M -> 0 is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V-ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat-flat if and only if M+ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m-injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and fiat modules coincide.