On modules and rings with the restricted minimum condition

Abstrakt

A module M satisfies the restricted minimum condition if M/N is Artinian for every essential submodule N of M and R is called a right RM-ring whenever it satisfies the restricted minimum condition as a right module. Several structural necessary conditions for particular classes of RM-rings are presented in the paper.

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.

Klíčová slova

• modules
• rings
• with
• restricted
• minimum
• condition