| Title:
|
Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
733-754 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The extension of a lattice ordered group $A$ by a generalized Boolean algebra $B$ will be denoted by $A_B$. In this paper we apply subdirect decompositions of $A_B$ for dealing with a question proposed by Conrad and Darnel. Further, in the case when $A$ is linearly ordered we investigate (i) the completely subdirect decompositions of $A_B$ and those of $B$, and (ii) the values of elements of $A_B$ and the radical $R(A_B)$. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
generalized Boolean algebra |
| Keyword:
|
extension |
| Keyword:
|
vector lattice |
| Keyword:
|
subdirect decomposition |
| Keyword:
|
value |
| Keyword:
|
radical |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 1164.06328 |
| idMR:
|
MR2291771 |
| . |
| Date available:
|
2009-09-24T11:37:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128101 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory.Third Edition, Providence, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[3] P. Conrad and M. R. Darnel: Generalized Boolean algebras in lattice ordered groups.Order 14 (1998), 295–319. MR 1644504 |
| Reference:
|
[4] P. Conrad and M. R. Darnel: Subgroups and hulls of Specker lattice-ordered groups.Czechoslovak Math. J 51 (2001), 395–413. MR 1844319, 10.1023/A:1013759300701 |
| Reference:
|
[5] C. Goffman: Remarks on lattice ordered groups and vector lattices. I. Carathéodory functions.Trans. Amer. Math. Soc. 88 (1958), 107–120. Zbl 0088.02602, MR 0097331 |
| Reference:
|
[6] J. Jakubík: Cardinal properties of lattice ordered groups.Fundamenta Math. 74 (1972), 85–98. MR 0302528, 10.4064/fm-74-2-85-98 |
| Reference:
|
[7] J. Jakubík: Torsion classes of Specker lattice ordered groups.Czechoslovak Math. J. 52 (2002), 469–482. MR 1923254, 10.1023/A:1021711326115 |
| Reference:
|
[8] J. Jakubík: On vector lattices of elementary Carathéodory functions.Czechoslovak Math. J 55 (2005), 223-236. MR 2121669, 10.1007/s10587-005-0017-x |
| Reference:
|
[9] J. Jakubík: Torsion classes and subdirect products of Carathéodory vector lattices.Math. Slovaca 56 (2006), 79–92. MR 2217581 |
| Reference:
|
[10] J. Jakubík: Generalized Boolean algebra extensions of lattice ordered groups.Tatra Mt. Math. Publ. 30 (2005), 1–19. MR 2190244 |
| Reference:
|
[11] F. Šik: Über subdirekte Summen geordneter Gruppen.Czechoslovak Math. J. 10 (1960), 400–424. MR 0123626 |
| . |
