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By Karakhanyan M.I., Khor'kova T.A.

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R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

1 1 2 4 5 7 9 10 11 Abstract We survey generalizations of Warfield’s 1968 Homomorphisms and Duality paper. Our main focus is in fixing a module A and examining when Warfield’s results hold relative to this fixed A. 1 Introduction Some of the most promising tools in the study of torsion-free abelian groups and modules have been the ideas developed in Warfield’s paper [49]. Specifically, the Hom/Tensor functors, H om(A, −) / − ⊗ A, and the contravariant functor H om(−, A), referred to as Warfield Duality, where A is a subgroup of the rational integers.

Self-Small Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Projectivity Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Class M A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Domains Which Support Warfield’s Results .

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