ON MODULES AND RINGS WITH THE RESTRICTED MINIMUM CONDITION
COLLOQUIUM MATHEMATICUM, cilt.140, sa.1, ss.75-86, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 140 Sayı: 1
- Basım Tarihi: 2015
- Doi Numarası: 10.4064/cm140-1-6
- Dergi Adı: COLLOQUIUM MATHEMATICUM
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.75-86
- Gazi Üniversitesi Adresli: Hayır
Özet
A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever R-R satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.