Abstract

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⊕Bas anR-module, thenA≅RκorB≅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.

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