## Homomorphisms of progenerator modules.(English)Zbl 0654.13016

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.
Reviewer: T.W.Hungerford

### MSC:

 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 13B99 Commutative ring extensions and related topics 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
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