$E$-algebras whose torsion part is not cyclic

Abstract

Abstract. We consider algebras A over a Dedekind domain R with the property A ∼ = EndAlg R A and generalize Schultz' structure theory of the case R = Z to Dedekind domains. We construct examples of mixed E(R)-algebras, which are non-split extensions of the submodule of elements infinitely divisible by the relevant prime ideals. This is also new in the case R = Z.