Mixed modules and endomorphisms over incomplete discrete valuation rings.

Abstract

Structure theorems are given for several classes of mixed modules over an arbitrary discrete valuation ring R, followed by results on the endomorphism algebras of mixed R-modules. The opening chapter introduces a fundamental embedding of R-modules into related modules over the p-adic completion of R, and the succeeding two chapters develop generalizations of the theory of simply presented modules of rank one and Warfield modules. Endomorphism algebras are considered in the penultimate chapter, where it is shown that the related modules over the completion of R are isomorphic if the underlying R-modules possess isomorphic endomorphism algebras. An isomorphism theorem for the endomorphism algebras of Warfield modules is deduced. Relevant constructions of mixed abelian groups are offered in the final chapter.