| Title:
|
On vector lattices of elementary Carathéodory functions (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
223-236 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we deal with the vector lattice $C(B)$ of all elementary Carathéodory functions corresponding to a generalized Boolean algebra $B$. (English) |
| Keyword:
|
generalized Boolean algebra |
| Keyword:
|
elementary Carathéodory functions |
| Keyword:
|
Specker lattice ordered group |
| Keyword:
|
$(\alpha, \beta)$-distributivity |
| Keyword:
|
complete distributivity |
| MSC:
|
06F20 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 1081.06021 |
| idMR:
|
MR2121669 |
| . |
| Date available:
|
2009-09-24T11:22:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127972 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory, Third Edition., Providence, 1967. MR 0227053 |
| Reference:
|
[2] P. Conrad: Lattice Ordered Groups.Tulane University, Tulane, 1970. Zbl 0258.06011 |
| Reference:
|
[3] P. Conrad and M. R. Darnel: Lattice-ordered groups whose lattices determine their additions.Trans. Amer. Math. Soc. 330 (1992), 575–598. MR 1031238, 10.1090/S0002-9947-1992-1031238-0 |
| Reference:
|
[4] P. F. Conrad and M. R. Darnel: Generalized Boolean algebras in lattice-ordered groups.Order 14 (1998), 295–319. MR 1644504, 10.1023/A:1006075129584 |
| Reference:
|
[5] P. F. Conrad and M. R. Darnel: Subgroups and hulls of Specker lattice-ordered groups.Czechoslovak Math. J (to appear). MR 1844319 |
| Reference:
|
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| Reference:
|
[7] C. Gofman: Remarks on lattice ordered groups and vector lattices. I. Carathéodory functions.Trans. Amer. Math. Soc. 88 (1958), 107–120. MR 0097331 |
| Reference:
|
[8] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen.Čas. pěst. mat. 83 (1959), 53–63. MR 0104740 |
| Reference:
|
[9] J. Jakubík: Cardinal properties of lattice ordered groups.Fundamenta Math. 74 (1972), 85–98. MR 0302528, 10.4064/fm-74-2-85-98 |
| Reference:
|
[10] J. Jakubík: Distributivity in lattice ordered groups.Czechoslovak Math. J. 22 (1972), 108–125. MR 0325487 |
| Reference:
|
[11] J. Jakubík: Torsion classes of Specker lattice ordered groups.Czechoslovak Math. J. 52 (2002), 469–482. MR 1923254, 10.1023/A:1021711326115 |
| Reference:
|
[12] R. Sikorski: Boolean Algebras.Second Edition, Springer-Verlag, Berlin, 1964. Zbl 0123.01303, MR 0177920 |
| Reference:
|
[13] E. C. Weinberg: Higher degrees of distributivity in lattices of continuous functions.Trans. Amer. Math. Soc. 114 (1962), 334–346. Zbl 0105.09401, MR 0138569, 10.1090/S0002-9947-1962-0138569-8 |
| . |
