On modules and rings with the restricted minimum condition

• Autorzy: M. Tamer Koşan , Jan Žemlička
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16D40: Free, projective, and flat modules and ideals
• 16E50: von Neumann regular rings and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 1
• Strony: 75-86

Daty

wydano

2015

Twórcy

autor

M. Tamer Koşan

• Department of Mathematics, Gebze Technical University, 41400 Gebze/Kocaeli, Turkey

autor

Jan Žemlička

• Department of Algebra, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/cm140-1-6