Homomorphisms of progenerator modules (Q1108333)

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.