On pairs of free modules over a Dedekind domain |
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Authors: | Saverio Cittadini Carlo Toffalori |
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Institution: | (1) Dipartimento di Matematica e Informatica, Università di Camerino, Via Madonna delle Carceri, 62032 Camerino, Italy |
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Abstract: | The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis
of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two
modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the
latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. Then we restrict our attention
to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable,
and that a few remarkable extensions of this theory are decidable.
Work performed under the auspices of GNSAGA-INDAM |
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Keywords: | |
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