Torsion-free duality is Warfield
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- by T. Faticoni, H. P. Goeters, C. Vinsonhaler and W. J. Wickless PDF
- Proc. Amer. Math. Soc. 125 (1997), 961-969 Request permission
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
- Frank W. Anderson and Kent R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, Vol. 13, Springer-Verlag, New York-Heidelberg, 1974. MR 0417223, DOI 10.1007/978-1-4684-9913-1
- H. P. Goeters, Warfield duality and extensions of modules over an integral domain, preprint.
- N. Jacobson, Basic Algebra II, W. H. Freeman, San Francisco (1983).
- E. L. Lady, A seminar on splitting rings for torsion free modules over Dedekind domains, Abelian group theory (Honolulu, Hawaii, 1983) Lecture Notes in Math., vol. 1006, Springer, Berlin, 1983, pp. 1–48. MR 722612, DOI 10.1007/BFb0103696
- E. L. Lady, Warfield duality and rank-one quasi-summands of tensor products of finite rank locally free modules over Dedekind domains, J. Algebra 121 (1989), no. 1, 129–138. MR 992320, DOI 10.1016/0021-8693(89)90089-6
- J. D. Reid, Warfield duality and irreducible groups, Abelian groups and noncommutative rings, Contemp. Math., vol. 130, Amer. Math. Soc., Providence, RI, 1992, pp. 361–370. MR 1176132, DOI 10.1090/conm/130/1176132
- C. Vinsonhaler and W. Wickless, Dualities for torsion-free abelian groups of finite rank, J. Algebra 128 (1990), no. 2, 474–487. MR 1036403, DOI 10.1016/0021-8693(90)90035-M
- R. B. Warfield Jr., Homomorphisms and duality for torsion-free groups, Math. Z. 107 (1968), 189–200. MR 237642, DOI 10.1007/BF01110257
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
- Received by editor(s): March 23, 1995
- Received by editor(s) in revised form: September 25, 1995
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1997 American Mathematical Society
- 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