Homomorphisms of progenerator modules and direct limits

Abstract EN

In 1988, F.

R.

DeMeyer and T.

J.

Ford [1] introduced a relation called homo-topy 0li the set of homomorphisms of progenerator modules over a commutative rmg R.

The set of homotopy classes forms a commutative monoid M.

(R), with operation induced by tensor product.

The assignment R —► M (R) determines an additive covariant functor from the category of commutative rings to the category °f c°mmutative monoids.

The monoid M (R) has been explicitly computed in [1] if R is a Dedekind domain.

In this paper we compute M (R) for the ring of all algebraic integers wh'ch is not a Dedekind domain but is a direct limit of Dedekind domains.