An application of set theory to the torsion product of abelian groups
Author: Patrick Keef
Journal: Proc. Amer. Math. Soc. 118 (1993), 735-738
MSC: Primary 20K10; Secondary 03E75, 20K40
MathSciNet review: 1146863
Full-text PDF Free Access
Abstract: The following problem of Fuchs is considered: relate the abelian groups and assuming for all reduced abelian groups . A complete characterization is obtained in any set-theoretic universe in which is valid for a proper class of regular cardinals .
-  Doyle Cutler, Abelian 𝑝-groups 𝐴 and 𝐵 such that 𝑇𝑜𝑟(𝐴,𝐺)≅𝑇𝑜𝑟(𝐵,𝐺), 𝐺 reduced, Proc. Amer. Math. Soc. 91 (1984), no. 1, 12–14. MR 735554, https://doi.org/10.1090/S0002-9939-1984-0735554-X
-  Paul C. Eklof and Alan H. Mekler, Almost free modules, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR 1055083
-  L. Fuchs, Infinite abelian groups, Vols. 1 and 2, Academic Press, New York, 1970 and 1973.
-  Paul Hill, Two problems of Fuchs concerning 𝑡𝑜𝑟 and ℎ𝑜𝑚, J. Algebra 19 (1971), 379–383. MR 0280586, https://doi.org/10.1016/0021-8693(71)90096-2
-  Roger Hunter, Fred Richman, and Elbert Walker, Warfield modules, Abelian group theory (Proc. Second New Mexico State Univ. Conf., Las Cruces, N. M., 1976) Springer, Berlin, 1977, pp. 87–123. Lecture Notes in Math., Vol. 616. MR 0506216
-  Patrick Keef, Some isomorphisms of abelian groups involving the Tor functor, Proc. Amer. Math. Soc. 110 (1990), no. 1, 27–37. MR 1030735, https://doi.org/10.1090/S0002-9939-1990-1030735-5
- D. Cutler, Abelian -groups and such that , reduced, Proc. Amer. Math. Soc. 91 (1984), 12-14. MR 735554 (85i:20059)
- P. Eklof and A. Mekler, Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990. MR 1055083 (92e:20001)
- L. Fuchs, Infinite abelian groups, Vols. 1 and 2, Academic Press, New York, 1970 and 1973.
- P. Hill, Two problems of Fuchs concerning tor and hom, J. Algebra 19 (1971), 379-383. MR 0280586 (43:6306)
- R. Hunter, F. Richman, and E. Walker, Warfield modules, Lecture Notes in Math., vol. 616, Springer-Verlag, Berlin and New York, 1977, pp. 87-123. MR 0506216 (58:22041)
- P. Keef, Some isomorphisms of abelian groups involving the Tor functor, Proc. Amer. Math. Soc. 110 (1990), 27-37. MR 1030735 (91b:20072)