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By Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)

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Extra info for Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976

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C. Megibben, On mixed groups of torsion-free rank one, Ill, J. Math. ii (1967), 134-144. 28. C. Megibben, Modules over an incomplete discrete valuation ring, Proc. Amer. Math. Soc. 19 (1968), 450-452. 29. R. J. Nunke, Modules of extensions over Dedekind rings, Ill. J. Math. 3 (1959), 222-241. 30. R. J. Nunke, Homology and direct sums of countable Abelian groups, Math. Zeits° 191 (1967), 182-212. 31. R. J. Nunke, Uniquely elongating modules, Proc. Conf. on Abelian Groups, (November, 1972), Symposia Mathematica 13, Academic Press, London, 1974, ppl 315-330.

In attempting to generalize Ulm's theorem, care must be taken to preserve relative Ulm invariants. Warfield [24]. This necessitates the following definition, due to 53 Definition. A decomposition basis X of a group A is a lower decomposition basis if, whenever the relative Ulm invariant f(a,p,A,[X]) is infinite (for a an ordinal or ~), then f(a,p,A) = f(a,p,A,[X]). Lemma 9. If A has a decomposition basis X, then there is a decomposition basis Y subordinate to X which is a lower decomposition basis.

41. E. A. Walker, Ulm's theorem for totally projective Amer. Math. Soc. 37 (1973), 387-392. 42. K. Alg. 17 (1971), 482-488. 43. R. B. , Homomorphisms and duality for torsion-free groups, Math. Zeits. 107 (1968), 189-200. 44. R. B. , An isomorphic refinement groups, Pacific J. , 34 (1970), 237-255. 45. R. B. , Invariants and a classification theorem for modules over a discrete valuation ring, University of Washington notes, 1971. 46. R. B. , Classification theorems for p-groups modules over a discrete valuation ring, Bull.

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