Year: 1970
Type: article
Abstract: It is proved that a commutative ring with $1$ has the property that every finitely presented module is a summand of a direct sum of cyclic modules if and only if it is locally a generalized valuation ring. A Noetherian ring has this property if and only if it is a direct product of a finite number of Dedekind domains and an Artinian principal ideal ring. Any commutative local ring which is not a generalized valuation ring has finitely presented indecomposable modules requiring arbitrarily large numbers of generators.
Author: R. B. Warfield
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2017432002