×

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


PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. Birkhoff, Abstract linear dependence and lattices,Amer. J. Math. 57 (1935), 800–804. · doi:10.2307/2371015
[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 · doi:10.1002/malq.19660120130
[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. · doi:10.1215/S0012-7094-38-00438-7
[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.
[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 · doi:10.1515/crll.1950.188.167
[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 · doi:10.2307/2371182
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.