We characterize the direct sums of uniserial modules over a valua-tion domain satisfying the
following property:(*) every element is contained in a pure uniserial submodule. We reduce …

Proof: 2 Let {u1, u2,...., u} be a basis of A. It is known that there exists a valuation w of K such
that R,, DR and M,,= A. We fix such a valuation w, and we label the ui so as to have w (ul)< w …

A module M is called 5~-pure-injective (= Z-algebraically compact) if every direct sum of
copies of M is pure-injective. In this paper we describe in detail the indecomposable …

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 …

The use of the finite topology on endomorphism rings - ScienceDirect Skip to main contentSkip
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The results obtained for non standard uniserial modules over valuation domains after the
first proof of their existence given by Shelah in 1984 are exposed: the other existence proofs …

KAPLANSKY'S PROBLEM ON VALUATION RINGS Page 1 proceedings of the american
mathematical society Volume 105, Number I, January 1989 KAPLANSKY'S PROBLEM ON …

Our present goal is to study those torsion modules over valuation domains which resemble
separable torsion abelian groups, namely, every finite set of elements can be embedded in …

For a discussion of our result, we will restrict to any non zero domain R with 1, ie R is a
commutative ring without zero-divisors~= 0. One interesting class of such rings are …

Rispondendo ad una questione posta da A. Orsatti in [8], si dà esempio di dualità, non
soddisfacente alle proprietà di estensione di caratteri, sopra un anello di valutazione …