On Infinite Direct Products of Copies of a Dedekind Domain Original Research Article

Let κ be an infinite cardinal number and letRκbe the direct product of κ copies of a Dedekind domainRwhich is not a field or a complete discrete valuation ring. IfRκequalsA circled plus Bas anR-module, thenA congruent with RκorB congruent with Rκ. If κ < μ, the lease measurable cardinal number, or R < κ = μ, then any direct summand ofRκis isomorphic to a direct product of ideals inR. An infinite direct product of nonzero ideals inRis isomorphic toRαfor some infinite α.