While investigating countably generated modules over a discrete valuation ring, J. Rotman
(1) singled out the class of taut modules as being worthy of a close look. He showed that in …

Throughout this paper, $ R $ will denote an arbitrary but fixed complete discrete valuation
ring. We shall show that two reduced $ R $-modules which are direct sums of countably …

This review paper is a continuation of two previous review papers devoted to properties of
modules over discrete valuation domains. The first part of this work was published in the …

In this paper R denotes a discrete valuation ring with prime p and R its padic completion.
Our mission here is to analyze and classify two kinds of mixed modules over R. Our …

An outline of the paper is as follows. In § 2 we introduce our new invariant, the K-sequence
of a subset of the module M, and discuss some of its elementary properties. In § 3 we state …

Henceforth we assume that Mt= T= Nt, M/T^ Q^ N/T, and that M and N are submodules of T*
with T*/M and T*/N torsion-free and divisible. Let M* he the P*-submodule of T* generated by …

Warfield has recently defined a new class of invariants for mixed modules over a discrete
valuation ring. These invariants, along with the Ulm invariants, enable Warfield to prove an …

JOSEPH ROTMAN l Introduction, A p-primary abelian group is a module over the p-adic
integers; thus Ulm's theorem can be viewed as a classification of reduced countably …

1. Introduction. In this paper we prove a structure theorem for reduced countably generated
R-modules of finite rank, where R is a complete discrete valuation ring (eg, the p-adic …

1. Introduction. The purpose of this paper is to announce the completion of a classification
(up to isomorphism) of all modules which are direct sums of countably generated modules …