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Torsion-free duality is Warfield

Author(s): T. Faticoni; H. P. Goeters; C. Vinsonhaler; W. J. Wickless
Journal: Proc. Amer. Math. Soc. 125 (1997), 961-969.
MSC (1991): Primary 20K15, 20K40, 20C05
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Abstract: We show that, under certain natural conditions, a duality discovered by R. B. Warfield, Jr., is the only duality on categories of finite-rank torsion-free modules over Dedekind domains.

References:

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H. P. Goeters, Warfield duality and extensions of modules over an integral domain, preprint.

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N. Jacobson, Basic Algebra II, W. H. Freeman, San Francisco (1983).

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E. L. Lady, A seminar on splitting rings for torsion free modules over Dedekind domains, Lecture Notes in Mathematics 1006 (1982), Springer-Verlag, New York, 1-48. MR 85f:13007

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C. Vinsonhaler and W. J. Wickless, Dualities for torsion-free abelian groups of finite rank, J. Algebra 128 (1990), 474-487. MR 91b:20076

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R. B. Warfield, Jr., Homomorphisms and duality for abelian groups, Math. Z. 107 (1968), 189-212. MR 38:5923

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Additional Information:

T. Faticoni
Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458

H. P. Goeters
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849

C. Vinsonhaler
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: vinson@uconnvm.uconn.edu

W. J. Wickless
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: wjwick@math.uconn.edu

DOI: 10.1090/S0002-9939-97-03619-8
PII: S 0002-9939(97)03619-8
Received by editor(s): March 23, 1995
Received by editor(s) in revised form: September 25, 1995
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1997, American Mathematical Society

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