Homomorphisms of progenerator modules
type: Item
instance of: scholarly article
title: Homomorphisms of progenerator modules
zbMATH Open document ID: 0654.13016
DOI: 10.1016/0021-8693(88)90167-6
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The authors study homomorphisms defined on progenerator modules over a commutative ring R. They define a relation on such homomorphisms, called homotopy, which is coarser than the usual relation of equivalence and show that the set M(R) of homotopy classes forms a commutative monoid under the operation induced by \(\otimes_ R\). The properties of the covariant functor M(-) from the category of commutative rings to the category of commutative monoids are developed. For a given ring R, a classification of homomorphisms is carried out by determining the algebraic structure of M(R) and then giving a representing homomorphism defined on free modules for each class in M(R). A complete description of M(R) is given in the case when R is a Dedekind domain.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13B99
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 4067065
zbMATH Keywords: homomorphisms
zbMATH Keywords: progenerator modules
zbMATH Keywords: homotopy
zbMATH Keywords: monoids
zbMATH Keywords: Dedekind domain
author: Frank R. DeMeyer
author: Timothy J. Ford
reviewed by: T. W. Hungerford
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90167-6
OpenAlex ID: W2010735648
cites work: \(K\)-theory and stable algebra
cites work: Q5340151
cites work: Separable algebras over commutative rings
cites work: Q4143433
cites work: Almost diagonal matrices over Dedekind domains
cites work: Decomposing Pairs of Modules
cites work: Projectivities over rings with many units
cites work: Q3849050
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description: scientific article; zbMATH DE number 4067065