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Glass, A. M. W.

Polars and their applications in directed interpolation groups. (English) Zbl 0235.06004

Trans. Am. Math. Soc. 166, 1-25 (1972).
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Cited in 10 Documents

MSC:

06F15 Ordered groups
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References:

[1] B. Banaschewski, On lattice-ordered groups, Fund. Math. 55 (1964), 113 – 122. · Zbl 0129.01803
[2] R. D. Byrd, Lattice-ordered groups, Ph.D. Dissertation, Tulane University, New Orleans, La., 1966. · Zbl 0182.04801
[3] Richard D. Byrd, \?-polars in lattice-ordered groups, Czechoslovak Math. J. 18 (93) (1968), 230 – 239 (English, with Loose Russian summary). · Zbl 0174.06004
[4] Richard D. Byrd, Paul Conrad, and Justin T. Lloyd, Characteristic subgroups of lattice-ordered groups, Trans. Amer. Math. Soc. 158 (1971), 339 – 371. · Zbl 0235.06006
[5] A. H. Clifford, A noncommutative ordinally simple linearly ordered group, Proc. Amer. Math. Soc. 2 (1952), 902 – 903. · Zbl 0044.01301
[6] Paul F. Conrad, Embedding theorems for abelian groups with valuations, Amer. J. Math. 75 (1953), 1 – 29. · Zbl 0050.02303 · doi:10.2307/2372611
[7] Paul Conrad, John Harvey, and Charles Holland, The Hahn embedding theorem for abelian lattice-ordered groups, Trans. Amer. Math. Soc. 108 (1963), 143 – 169. · Zbl 0126.05002
[8] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. · Zbl 0137.02001
[9] L. Fuchs, Riesz groups, Ann. Scuola Norm. Sup. Pisa (3) 19 (1965), 1 – 34. · Zbl 0125.28703
[10] A. M. W. Glass, Which abelian groups can support a directed, interpolation order?, Proc. Amer. Math. Soc. 31 (1972), 395 – 400. · Zbl 0235.06009
[11] -, The lattice of convex directed subgroups of a directed, interpolation group (unpublished paper(\( ^{1}\))).
[12] P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595 – 622. · Zbl 0091.02501 · doi:10.1112/plms/s3-9.4.595
[13] Charles Holland, The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10 (1963), 399 – 408. · Zbl 0116.02102
[14] Paul Jaffard, Sur le spectre d’un groupe réticulé et l’unicité des réalisations irréductibles, Ann. Univ. Lyon. Sect. A (3) 22 (1959), 43 – 47 (French). · Zbl 0103.01601
[15] P. Lorenzen, Abstrakte Begründung der multiplikativen Idealtheorie, Math. Z. 45 (1939), 533 – 553 (German). · JFM 65.0101.01 · doi:10.1007/BF01580299
[16] D. Papert, A representation theory for lattice-groups, Proc. London Math. Soc. (3) 12 (1962), 100 – 120. · Zbl 0152.01401 · doi:10.1112/plms/s3-12.1.100
[17] J. Roger Teller, A theorem on Riesz groups, Trans. Amer. Math. Soc. 130 (1968), 254 – 264. · Zbl 0155.06002
[18] Elliot Carl Weinberg, Embedding in a divisible lattice-ordered group, J. London Math. Soc. 42 (1967), 504 – 506. · Zbl 0157.36802 · doi:10.1112/jlms/s1-42.1.504
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