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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
MathSciNet review:
1353383
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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:
- [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
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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