Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants

Abstract

Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3]. Finally, we obtain similar results for the dual class of max modules.

Key Words:

• Endomorphism ring
• Loewy module
• Max module
• Module
• Semilocal ring

2010 Mathematics Subject Classification:

• Primary: 16P20
• Secondary: 16D80, 16L30, 18P60

Notes

Communicated by S. Bazzoni.