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Title: Lattice formulation of general algebraic dependence (English)
Author: Dlab, Vlastimil
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 20
Issue: 4
Year: 1970
Pages: 603-615
Summary lang: English
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Category: math
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MSC: 06.30
idZBL: Zbl 0247.06006
idMR: MR0268093
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Date available: 2008-06-09T13:48:40Z
Last updated: 2016-04-06
Stable URL: http://hdl.handle.net/10338.dmlcz/100986
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Reference: [2] V. Dlab: General algebraic dependence relations.Publ. Math. Debrecen 9 (1962), 324-355. Zbl 0119.01602, MR 0150078
Reference: [3] V. Dlab: General algebraic dependence structures and some applications.Colloq. Math. 14 (1966), 265-273. Zbl 0136.26302, MR 0183666
Reference: [4] V. Dlab: Algebraic dependence structures.Z. Math. Logik Grundlagen Math. 12 (1966), 345-377. Zbl 0144.00901, MR 0214527, 10.1002/malq.19660120130
Reference: [5] V. Dlab: Dependence over modules.Czechoslovak Math. J. 16 (91) (1966), 137-157. Zbl 0139.26101, MR 0190188
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Reference: [7] V. Dlab: Matrix representation of torsion-free rings.Czechoslovak Math. J. 19 (94) (1969), 284-298. Zbl 0182.36902, MR 0245612
Reference: [8] V. Dlab: Lattice representation of general algebraic dependence.Math. Systems Theory 4 (1969), 289-299. Zbl 0199.32401, MR 0252300, 10.1007/BF01691058
Reference: [9] L. Fuchs: Abelian groups.Akadémiai Kiadó. Budapest, 1958. Zbl 0091.02704
Reference: [10] M. L. Dubreil-Jacotin L. Lesieur, R. Croisot: Leçons sur la théorie des treillis.Gauthier-Villars, Paris 1953. MR 0057838
Reference: [11] H. Hermes: Einführung in die Verbandstheorie.Springer, 1955. Zbl 0064.02901, MR 0067082
Reference: [12] E. Marczewski: A general scheme of the notions of independence in mathematics.Bull. Acad. Polon. Sci., Sér. sci math., astronom. et phys. 6 (1958), 731 - 736. Zbl 0088.03001, MR 0104610
Reference: [13] E. Marczewski: Independence in some abstract algebras.ibid. 7 (1959), 611 - 616. Zbl 0093.03504, MR 0115954
Reference: [14] W. Narkiewicz: Independence in a certain class of abstract algebras.Fund. Math. 50 (1960), 333-340. MR 0136566
Reference: [15] J. von Neumann: Continuous geometry.Princeton University Press, 1960. Zbl 0171.28003, MR 0120174
Reference: [16] D. E. Rutherford: Introduction to lattice theory.Oliver & Boyd, Edinburgh, 1965. Zbl 0127.24904, MR 0176942
Reference: [17] J. Schmidt: Einige algebraische Äquivalente zum Auswahlaxiom.Fund. Math. 50 (1960), 485-496. MR 0139558
Reference: [18] G. Szász: Introduction to lattice theory.3rd ed.. Academic Press and Akadémiai Kiadó, 1963. MR 0166118
Reference: [19] H. Whitney: On the abstract properties of linear dependence.Amer. J. Math. 57 (1935), 509-533. Zbl 0012.00404, MR 1507091, 10.2307/2371182
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