| Title:
|
Complete distributivity of lattice ordered groups and of vector lattices (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
889-896 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the possibility of a regular embedding of a lattice ordered group into a completely distributive vector lattice. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
vector lattice |
| Keyword:
|
complete distributivity |
| Keyword:
|
regular embedding |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 0998.06013 |
| idMR:
|
MR1864049 |
| . |
| Date available:
|
2009-09-24T10:48:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127693 |
| . |
| Reference:
|
[1] S. J. Bernau: Unique representation of Archimedean lattice groups and normal Archimedean lattice rings.Proc. London Math. Soc. 15 (1965), 599–631. MR 0182661 |
| Reference:
|
[2] G. Birkhoff: Lattice Theory. Revised Edition.American Mathematical Society, Providence, 1948. MR 0029876 |
| Reference:
|
[3] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[4] P. Conrad and D. McAlister: The completion of a lattice ordered group.J. Austral. Math. Soc. 9 (1969), 182–208. MR 0249340, 10.1017/S1446788700005760 |
| Reference:
|
[5] J. Jakubík: Representation and extension of $\ell $-groups.Czechoslovak Math. J. 13 (1963), 267–283. (Russian) MR 0171865 |
| Reference:
|
[6] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen.Časopis pěst. matem. 84 (1959), 53–63. MR 0104740 |
| Reference:
|
[7] J. Jakubík: Die Dedekindschen Schnitte im direkten Product von halbgeordneten Gruppen.Mat. fyz. časopis Slovenskej akad. vied 16 (1966), 329–336. MR 0210638 |
| Reference:
|
[8] J. Jakubík: Distributivity in lattice ordered groups.Czechoslovak Math. J. 22 (1972), 108–125. MR 0325487 |
| Reference:
|
[9] L. V. Kantorovich, B. Z. Vulikh and A. G. Pinsker: Functional Analysis in Semiordered Spaces.Moskva, 1950. (Russian) |
| Reference:
|
[10] M. A. Lapellere and A. Valente: Embedding of Archimedean $\ell $-groups in Riesz spaces.Atti Sem. Mat. Fis. Univ. Modena 46 (1998), 249–254. MR 1628633 |
| Reference:
|
[11] W. A. J. Luxemburg and A. C. Zaanen: Riesz Spaces, Vol. 1.North-Holland Publishing Company, Amsterdam, 1971. MR 0511676 |
| Reference:
|
[12] F. Maeda and T. Ogasavara: Representation of vector lattices.J. Hiroshima Univ., Ser. A 12 (1942), 17–35. MR 0029087, 10.32917/hmj/1558306491 |
| Reference:
|
[13] R. S. Pierce: Distributivity in Boolean algebras.Pacific. J. Math. 7 (1957), 983–992. Zbl 0086.02803, MR 0089180, 10.2140/pjm.1957.7.983 |
| Reference:
|
[14] A. G. Pinsker: Extensions of semiordered groups and spaces.Uch. Zap. Leningrad. Gos. Ped. Inst. 86 (1949), 285–315. (Russian) |
| Reference:
|
[15] R. H. Redfield: Archimedean and basic elements in completely distributive lattice-ordered groups.Pacific. J. Math. 63 (1976), 247–253. Zbl 0324.06007, MR 0412074, 10.2140/pjm.1976.63.247 |
| Reference:
|
[16] R. Sikorski: Boolean Algebras.Second Edition, Springer Verlag, Berlin, 1964. Zbl 0123.01303, MR 0177920 |
| Reference:
|
[17] E. C. Smith jr. and A. Tarski: Higher degrees of distributivity and completeness in Boolean algebras.Trans. Amer. Math. Soc. 84 (1957), 230–257. MR 0084466, 10.1090/S0002-9947-1957-0084466-4 |
| Reference:
|
[18] B. Z. Vulikh: Introduction to the Theory of Semiordered Spaces.(In Russian; English translation: Introduction to the Theory of Partially Ordered Spaces, Groningen 1967), Moskva, 1961. |
| Reference:
|
[19] K. Yosida: On the representation of the vector lattice.Proc. Acad. Tokyo 18 (1942), 339–342. Zbl 0063.09070, MR 0015378 |
| . |
