×

Global Warfield groups. (English) Zbl 0471.20038


MSC:

20K25 Direct sums, direct products, etc. for abelian groups
20K21 Mixed groups
20K27 Subgroups of abelian groups
20K10 Torsion groups, primary groups and generalized primary groups
20K20 Torsion-free groups, infinite rank
Full Text: DOI

References:

[1] D. Arnold, R. Hunter, and F. Richman, Global Azumaya theorems in additive categories, J. Pure Appl. Algebra 16 (1980), no. 3, 223 – 242. · Zbl 0443.18014 · doi:10.1016/0022-4049(80)90026-2
[2] David Arnold, Roger Hunter, and Elbert Walker, Direct sums of cyclic valuated groups, Symposia Mathematica, Vol. XXIII (Conf. Abelian Groups and their Relationship to the Theory of Modules, INDAM, Rome, 1977) Academic Press, London-New York, 1979, pp. 77 – 84. · Zbl 0419.20042
[3] Peter Crawley and Alfred W. Hales, The structure of torsion abelian groups given by presentations, Bull. Amer. Math. Soc. 74 (1968), 954 – 956. · Zbl 0194.04502
[4] László Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. · Zbl 0257.20035
[5] Roger H. Hunter, Balanced subgroups of abelian groups, Trans. Amer. Math. Soc. 215 (1976), 81 – 98. · Zbl 0321.20035
[6] Roger Hunter, Fred Richman, and Elbert Walker, Simply presented valuated abelian \?-groups, J. Algebra 49 (1977), no. 1, 125 – 133. · Zbl 0383.20038 · doi:10.1016/0021-8693(77)90272-1
[7] Roger Hunter, Fred Richman, and Elbert Walker, Existence theorems for Warfield groups, Trans. Amer. Math. Soc. 235 (1978), 345 – 362. · Zbl 0368.20034
[8] 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. · Zbl 0376.13007
[9] Irving Kaplansky and George W. Mackey, A generalization of Ulm’s theorem, Summa Brasil. Math. 2 (1951), 195 – 202. · Zbl 0054.01803
[10] Charles K. Megibben, On mixed groups of torsion-free rank one, Illinois J. Math. 11 (1967), 134 – 144. · Zbl 0139.25204
[11] Charles Megibben, Modules over an incomplete discrete valuation ring, Proc. Amer. Math. Soc. 19 (1968), 450 – 452. · Zbl 0163.28903
[12] F. Richman, The constructive theory of \( KT\)-modules, Pacific J. Math. 61 (1975), 621-637. · Zbl 0305.02046
[13] Fred Richman and Elbert A. Walker, Valuated groups, J. Algebra 56 (1979), no. 1, 145 – 167. · Zbl 0401.20049 · doi:10.1016/0021-8693(79)90330-2
[14] Joseph Rotman, Mixed modules over valuations rings, Pacific J. Math. 10 (1960), 607 – 623. · Zbl 0094.02303
[15] Joseph Rotman, Torsion-free and mixed abelian groups, Illinois J. Math. 5 (1961), 131 – 143. · Zbl 0101.01901
[16] Joseph Rotman and Ti Yen, Modules over a complete discrete valuation ring, Trans. Amer. Math. Soc. 98 (1961), 242 – 254. · Zbl 0101.02801
[17] R. O. Stanton, An invariant for modules over a discrete valuation ring, Proc. Amer. Math. Soc. 49 (1975), 51 – 54. · Zbl 0283.13003
[18] -, Relative \( S\)-invariants, preprint.
[19] Robert O. Stanton, Decompostion bases and Ulm’s theorem, Abelian group theory (Proc. Second New Mexico State Univ. Conf., Las Cruces, N.M., 1976) Springer, Berlin, 1977, pp. 39 – 56. Lecture Notes in Math., Vol. 616.
[20] Robert O. Stanton, Infinite decomposition bases, Pacific J. Math. 70 (1977), no. 2, 549 – 566. · Zbl 0344.20041
[21] -, Decomposition of modules over a discrete valuation ring, J. Austrialian Math. Soc. (to appear).
[22] Robert O. Stanton, Almost-affable abelian groups, J. Pure Appl. Algebra 15 (1979), no. 1, 41 – 52. · Zbl 0407.20044 · doi:10.1016/0022-4049(79)90039-2
[23] -, \( S\)-groups, preprint.
[24] -, Warfield groups and \( S\)-groups, preprint.
[25] Elbert A. Walker, Ulm’s theorem for totally projective groups, Proc. Amer. Math. Soc. 37 (1973), 387 – 392. · Zbl 0257.20039
[26] Kyle D. Wallace, On mixed groups of torsion-free rank one with totally projective primary components, J. Algebra 17 (1971), 482 – 488. · Zbl 0215.39902 · doi:10.1016/0021-8693(71)90005-6
[27] R. B. Warfield, Jr., Invariants and a classification theorem for modules over a discrete valuation ring, Univ. of Washington notes, 1971.
[28] R. B. Warfield Jr., Classification theorems for \?-groups and modules over a discrete valuation ring, Bull. Amer. Math. Soc. 78 (1972), 88 – 92. · Zbl 0231.13004
[29] -, Simply presented groups, Proc. Sem. Abelian Group Theory, Univ. of Arizona lecture notes, 1972.
[30] -, Simply presented groups, Univ. of Washington notes, January 1974.
[31] R. B. Warfield Jr., A classification theorem for abelian \?-groups, Trans. Amer. Math. Soc. 210 (1975), 149 – 168. · Zbl 0324.20058
[32] R. B. Warfield Jr., Classification theory of abelian groups. I. Balanced projectives, Trans. Amer. Math. Soc. 222 (1976), 33 – 63. · Zbl 0358.20065
[33] -, Classification theory of abelian groups. II. Local theory, preprint.
[34] Robert B. Warfield Jr., The structure of mixed abelian groups, Abelian group theory (Proc. Second New Mexico State Univ. Conf., Las Cruces, N.M., 1976) Springer, Berlin, 1977, pp. 1 – 38. Lecture Notes in Math., Vol. 616.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.