Self-pure-generators over Dedekind domains |
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Authors: | Simion Breaz |
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Institution: | Babe?-Bolyai University, Faculty of Mathematics and Computer Science, Str. Mihail Kog?lniceanu 1, 400084 Cluj-Napoca, Romania |
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Abstract: | We prove that all pure submodules of a finite rank torsion-free module A over a Dedekind domain are A-generated (i.e. A is a self-pure-generator) if and only if A has a rank 1 direct summand B such that is the inner type of A. This result is applied to describe the direct products of torsion-free groups of finite rank which are self-pure-generators. |
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Keywords: | 13C05 20K15 Dedekind domain Finite rank torsion-free module Pure submodule Self-pure-generator Type |
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