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A simple proof of uniqueness for torsion modules over principal ideal domains.

J. L. García Roig (1985)

Stochastica

The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.

Kaplansky classes

Edgar E. Enochs, J. A. López-Ramos (2002)

Rendiconti del Seminario Matematico della Università di Padova

On a non-vanishing Ext

Laszlo Fuchs, Saharon Shelah (2003)

Rendiconti del Seminario Matematico della Università di Padova

On torsion Gorenstein injective modules

Okyeon Yi (1998)

Archivum Mathematicum

In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if D is a Gorenstein integral domain and M is a left D -module, then the torsion submodule t G M of Gorenstein injective envelope G M of M is also Gorenstein injective. We can also show that if M is a torsion D -module of a Gorenstein injective integral domain D , then the Gorenstein injective envelope G M of M is torsion.

Relative multiplication and distributive modules

José Escoriza, Blas Torrecillas (1997)

Commentationes Mathematicae Universitatis Carolinae

We study the construction of new multiplication modules relative to a torsion theory τ . As a consequence, τ -finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.

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