Abstract
This article presents a new method, based on the theory of integer representations, for investigating torsion free abelian groups of finite rank. In particular, it is proved that the direct decompositions of such groups are in bijective correspondence with the decompositions of vectors of some cone in an integer lattice into the sum of vectors in the lattice.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 135–153, 1989.
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Yakovlev, A.V. Torsion free Abelian groups of finite rank and their direct decompositions. J Math Sci 57, 3524–3533 (1991). https://doi.org/10.1007/BF01100125
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DOI: https://doi.org/10.1007/BF01100125