| 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 |
| . |
| Category:
|
math |
| . |
| MSC:
|
06.30 |
| idZBL:
|
Zbl 0247.06006 |
| idMR:
|
MR0268093 |
| DOI:
|
10.21136/CMJ.1970.100986 |
| . |
| Date available:
|
2008-06-09T13:48:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100986 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice theory.3rd ed., Amer. Math. Soc. Colloq. Publ. No 25, Providence, R. I., 1967. Zbl 0153.02501, MR 0227053 |
| 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, 10.4064/cm-14-1-265-273 |
| 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 |
| Reference:
|
[6] V. Dlab: Rank theory of modules.Fund. Math. 64 (1969), 313-324. Zbl 0192.38001, MR 0246909, 10.4064/fm-64-3-313-324 |
| 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, 10.4064/fm-50-4-333-340 |
| 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, 10.4064/fm-50-5-485-496 |
| 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 |
| . |
