| Title:
|
Weak $\sigma $-distributivity of lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
151-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove that the collection of all weakly distributive lattice ordered groups is a radical class and that it fails to be a torsion class. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
weak $\sigma $-distributivity |
| Keyword:
|
radical class |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 0978.06009 |
| idMR:
|
MR1826478 |
| DOI:
|
10.21136/MB.2001.133918 |
| . |
| Date available:
|
2009-09-24T21:48:25Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133918 |
| . |
| Reference:
|
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| Reference:
|
[2] A. Boccuto: Integration in Riesz spaces with respect to $(D)$-convergence.Tatra Mountains Math. Publ. 10 (1997), 33–54. Zbl 0918.28010, MR 1469280 |
| Reference:
|
[3] M. Darnel: Closure operations on radicals of lattice ordered groups.Czechoslovak Math. J. 37 (1987), 51–64. MR 0875127 |
| Reference:
|
[4] D. Gluschankof: Cyclic ordered groups and $MV$-algebras.Czechoslovak Math. J. 43 (1993), 249–263. Zbl 0795.06015, MR 1211747 |
| Reference:
|
[5] J. Jakubík: Radical mappings and radical classes of lattice ordered groups.Symposia Math vol. 21, Academic Press, New York-London, 1977, pp. 451–477. MR 0491397 |
| Reference:
|
[6] J. Jakubík: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44 (1994), 725–739. |
| Reference:
|
[7] J. Jakubík: Radical classes of $MV$-algebras.Czechoslovak Math. J. 49 (1999), 191–211. MR 1676805, 10.1023/A:1022428713092 |
| Reference:
|
[8] J. Martinez: Torsion theory for lattice-ordered groups.Czechoslovak Math. J. 25 (1975), 284–299. Zbl 0321.06020, MR 0389705 |
| Reference:
|
[9] D. Mundici: Interpretation of $AFC^*$-algebras in Łukasziewicz sentential calculus.J. Functional Anal. 65 (1986), 15–53. MR 0819173, 10.1016/0022-1236(86)90015-7 |
| Reference:
|
[10] B. Riečan, T. Neubrunn: Integral, Measure and Ordering.Kluwer Publ., Dordrecht, 1997. MR 1489521 |
| Reference:
|
[11] Dao-Rong Ton: Product radical classes of $\ell $-groups.Czechoslovak Math. J. 43 (1992), 129–142. MR 1152176 |
| . |
