ON MODULES AND RINGS WITH THE RESTRICTED MINIMUM CONDITION

Kosan M. T., Zemlicka J.

COLLOQUIUM MATHEMATICUM, cilt.140, sa.1, ss.75-86, 2015 (SCI-Expanded) identifier identifier

  • 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.