Torsion-free duality is Warfield

Authors:
T. Faticoni, H. P. Goeters, C. Vinsonhaler and W. J. Wickless

Journal:
Proc. Amer. Math. Soc. **125** (1997), 961-969

MSC (1991):
Primary 20K15, 20K40, 20C05

DOI:
https://doi.org/10.1090/S0002-9939-97-03619-8

MathSciNet review:
1353383

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Abstract | References | Similar Articles | Additional Information

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.

**[AF]**F. W. Anderson and K. R. Fuller,*Rings and categories of modules*, Springer-Verlag, GTM**13**(1974), Springer-Verlag, New York. MR**54:5281****[G]**H. P. Goeters,*Warfield duality and extensions of modules over an integral domain*, preprint.**[J]**N. Jacobson,*Basic Algebra*II, W. H. Freeman, San Francisco (1983).**[L1]**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****[L2]**-,*Warfield duality and rank one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains*, J. Algebra**121**(1989), 129-138. MR**90k:13007****[R]**J. D. Reid,*Warfield duality and irreducible groups*, Cont. Math.**130**(1992), American Math. Society, Providence, 361-370. MR**93j:20114****[VW]**C. Vinsonhaler and W. J. Wickless,*Dualities for torsion-free abelian groups of finite rank*, J. Algebra**128**(1990), 474-487. MR**91b:20076****[W]**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**

Email:
wjwick@math.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03619-8

Received by editor(s):
March 23, 1995

Received by editor(s) in revised form:
September 25, 1995

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society