Abstract
Let R be a commutative ring, with a unity 1 not equal to 0 and M a unitary left R-module. In this paper we give some properties of an FGS-module. After that we give others important characterizations. Indeed, we first show that M is a local FGS-module if and only if it is of finite representation type. Secondly, we show that M is a prime FGS-module if and only if it is a serial type module and of finite length if and only if it is a finite representation type module.
Highlights
Let R be a commutative ring with 1 0 as unity and M a left module over R
We first show that M is a local FGS -module if and only if it is of finite representation type
We show that M is a prime FGS -module if and only if it is a serial type module and of finite length if and only if it is a finite representation type module
Summary
Let R be a commutative ring with 1 0 as unity and M a left module over R. We first show that M is a local FGS -module if and only if it is of finite representation type. We characterize the modules for which every Hopfian object of σ[M] is finitely generated. A module is said serial type if every object of σ[M] is direct sum of uniserial modules of finite length.
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