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Dlab, Vlastimil

Lattice representation of general algebraic dependence. (English) Zbl 0199.32401

Math. Syst. Theory 3, 289-299 (1969).
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Keywords:

general algebraic structures
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\textit{V. Dlab}, Math. Syst. Theory 3, 289--299 (1969; Zbl 0199.32401)
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References:

[1] G. Birkhoff, Abstract linear dependence and lattices,Amer. J. Math. 57 (1935), 800–804. · JFM 61.1027.01
[2] G. Birkhoff,Lattice Theory, 3rd ed., Amer. Math. Soc. Colloq. Publ. No. 25, Providence, R.I., 1967.
[3] V. Dlab, General algebraic dependence relations,Publ. Math. Debrecen 9 (1962), 324–355. · Zbl 0119.01602
[4] V. Dlab, General algebraic dependence structures and some applications,Colloq. Math. 14 (1966), 265–273. · Zbl 0136.26302
[5] V. Dlab, Algebraic dependence structures,Z. Math. Logik Grundlagen Math. 12 (1966), 345–377. · Zbl 0144.00901
[6] V. Dlab, Dependence over modules,Czechoslovak Math. J. 16(91 (1966), 137–157. · Zbl 0139.26101
[7] V. Dlab, Rank theory of modules,Fund. Math. (to appear). · Zbl 0192.38001
[8] V. Dlab, Matrix representation of torsion-free rings,Czechoslovak Math. J. (to appear). · Zbl 0182.36902
[9] V. Dlab, Lattice formulation of general algebraic dependence (to appear). · Zbl 0247.06006
[10] L. Fuchs,Abelian groups, Akadémiai Kiadó, Budapest, 1958.
[11] S. Mac Lane, A lattice formulation for transcendence degrees andp-bases,Duke Math. J. 4 (1938), 455–468. · JFM 64.0072.02
[12] T. Nakasawa, Zur Axiomatik der linearen Abhängigkeit I, II, III.Rep. Tokyo Bunr. Daigaku 2 (1935), 235–255;3 (1936), 45–69;3 (1936), 123–136. · JFM 61.1341.03
[13] G. Szász,Introduction to Lattice Theory, 3rd ed., Academic Press and Akadémiai Kiadó, 1963.
[14] T. Szele, Ein Analogon der Körpertheorie für abelsche Gruppen,J. Reine Angew. Math. 188 (1950), 167–192. · Zbl 0054.01003
[15] B. L. van der Waerden,Moderne Algebra I, 2nd ed., Springer, 1937.
[16] H. Whitney, On the abstract properties of linear dependence,Amer. J. Math. 57 (1935), 509–533. · Zbl 0012.00404
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