Dualities for torsion-free abelian groups of finite rank
Journal of Algebra, 1990 Two well-known dualities have been very useful in the study of torsionfree abelian groups of finite rank: Warlield duality for locally free groups and Arnold duality for quotient divisible groups [Wa, Ar]. In this note we establish a duality, on classes of torsion-free abelian groups of finite rank, which generalizes both Warlield and Arnold duality ...
C. Vinsonhaler, W. Wickless
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The classification problem for S-local torsion-free abelian groups of finite rank [PDF]
Advances in Mathematics, 2010 AbstractSuppose that n⩾2 and that S, T are sets of primes. Then the classification problem for the S-local torsion-free abelian groups of rank n is Borel reducible to the classification problem for the T-local torsion-free abelian groups of rank n if and only if S⊆T.
Simon Thomas
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An equivalence relation for torsion-free abelian groups of finite rank
Journal of Algebra, 1992 The equivalence relation in question is defined as follows: let \({^\perp G}=\{X:\Hom(X,G)=0\}\). Then \(G\) is equivalent to \(H\) if and only if \({^\perp G}={^\perp H}\). Since this relation is coarser than quasi-isomorphism, it is useful in classifying torsion-free abelian groups.
W. Wickless
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Duality of the categories of torsion-free Abelian groups of finite rank and quotient divisible Abelian groups [PDF]
Journal of Mathematical Sciences, 2010 A new approach to the description of quotient divisible Abelian groups is proposed. This approach allowed us to give an explicit and natural proof of the duality of the categories of torsion-free Abelian groups of finite rank and quotient divisible Abelian groups with distinguished basic subgroups. Bibliography: 3 titles.
A. V. Yakovlev
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Endomorphism rings and subgroups of finite rank torsion-free Abelian groups [PDF]
Rocky Mountain Journal of Mathematics, 1982 Donald M. Arnold
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Solving logistic tasks by parallelizing algorithms of the theory of direct decompositions of torsion-free abelian groups [PDF]
E3S Web of Conferences, 2023 The paper considers the principles of parallelization at marshalling yards and determines their importance. There are presented the methods for direct decompositions of torsion-free Abelian groups of finite rank.
Blagoveshchenskaya E. +2 more
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A theorem on quasi-pure-projective torsion free abelian groups of finite rank [PDF]
Pacific Journal of Mathematics, 1980 C. Vinsonhaler, W. Wickless
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A cancellation criterion for finite-rank torsion-free abelian groups [PDF]
Proceedings of the American Mathematical Society, 1985 In this paper, a necessary ring-theoretical criterion is given for a finite-rank torsion-free abelian group to have the cancellation property. This generalizes results obtained by L. Fuchs and F. Loonstra [5] for the rank-one case and resolves the cancellation problem for strongly indecomposable groups.
H. J. Stelzer
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Abelian Rank of Normal Torsion-Free Finite Index Subgroups of Polyhedral Groups [PDF]
Transactions of the American Mathematical Society, 1985 Suppose that P P is a convex polyhedron in the hyperbolic 3 3 -space with finite volume and P P has integer ( > 1 ) ( > 1) submultiples of π \pi as dihedral angles.
Youn W. Lee
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The cotypeset of a torsion-free Abelian group of finite rank
Journal of Algebra, 1983 For a discussion of types and for basic definitions and notations see [ 7 1. In 1961 Beaumont and Pierce [4] posed the problem of finding necessary and sufficient conditions for a (necessarily finite or countable) set T of types to be realized as T = typeset G for some G of rank two.
C. Vinsonhaler, W. Wickless
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