| Title:
|
Strong projectability of lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
957-973 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove that the lateral completion of a projectable lattice ordered group is strongly projectable. Further, we deal with some properties of Specker lattice ordered groups which are related to lateral completeness and strong projectability. (English) |
| Keyword:
|
Lattice ordered group |
| Keyword:
|
projectability |
| Keyword:
|
strong projectability |
| Keyword:
|
lateral completion |
| Keyword:
|
orthocompletion |
| Keyword:
|
Specker lattice ordered group |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 1081.06023 |
| idMR:
|
MR2184377 |
| . |
| Date available:
|
2009-09-24T11:29:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128038 |
| . |
| Reference:
|
[1] S. J. Bernau: The lateral completion of an arbitrary lattice group.J. Austral. Math. Soc. 19 (1975), 263–289. Zbl 0314.06011, MR 0384640, 10.1017/S1446788700031463 |
| Reference:
|
[2] S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups.J. London Math. Soc. 12 (1976), 320–322. Zbl 0333.06008, MR 0401579, 10.1112/jlms/s2-12.3.320 |
| Reference:
|
[3] R. D. Bleier: The ${\mathrm SP}$-hull of a lattice-ordered group.Canadian J. Math. 26 (1974), 866–878. MR 0345891, 10.4153/CJM-1974-081-x |
| Reference:
|
[4] R. D. Bleier: The orthocompletion of a lattice-ordered group.Indagationes Math. 38 (1976), 1–7. Zbl 0329.06013, MR 0401581, 10.1016/1385-7258(76)90000-7 |
| Reference:
|
[5] D. Byrd and T. J. Lloyd: A note on lateral completion in lattice ordered groups.J. London Math. Soc. 1 (1969), 358–362. MR 0249339, 10.1112/jlms/s2-1.1.358 |
| Reference:
|
[6] D. A. Chambless: Representation of the projectable and strongly projectable hulls of a lattice ordered group.Proc. Amer. Math. Soc. 19 (1975), 263–289. MR 0295990 |
| Reference:
|
[7] P. F. Conrad: Lateral completion of lattice ordered groups.Proc. London Math. Soc. 19 (1969), 444–480. MR 0244125, 10.1112/plms/s3-19.3.444 |
| Reference:
|
[8] P. F. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[9] P. F. Conrad: The hulls of representable $\ell $-groups and $f$-rings.J. Austral. Math. Soc. 16 (1973), 385–415. MR 0344173, 10.1017/S1446788700015391 |
| Reference:
|
[10] P. F. Conrad: Epi-Archimedean $\ell $-groups.Czechoslovak Math. J. 24 (1974), 192–218. MR 0347701 |
| Reference:
|
[11] 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:
|
[12] M. R. Darnel: The Theory of Lattice Ordered Groups.Marcel Dekker, New York-Basel, 1995. MR 1304052 |
| Reference:
|
[13] J. Jakubík: Representations and extensions of $\ell $-groups.Czechoslovak Math. J. 13 (1963), 267–282. (Russian) |
| Reference:
|
[14] J. Jakubík: Lateral and Dedekind completions of strongly projectable lattice ordered groups.Czechoslovak Math. J 47 (1997), 511–523. MR 1461430, 10.1023/A:1022419703077 |
| Reference:
|
[15] J. Jakubík: Orthogonal hull of a strongly projectable lattice ordered group.Czechoslovak Math. J. 28 (1978), 484–504. MR 0505957 |
| Reference:
|
[17] J. Jakubík: Torsion classes of Specker lattice ordered groups.Czechoslovak Math. J. 52 (2002), 469–482. MR 1923254, 10.1023/A:1021711326115 |
| Reference:
|
[18] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen.Čas. pěst. mat. 84 (1959), 53–63. MR 0104740 |
| Reference:
|
[19] K. Keimel: Représentation de groupes et d’anneaux réticulés par des sections dans des faisceaux.PhD. Thesis, Université de Paris, 1970. Zbl 0249.06002 |
| Reference:
|
[20] G. Ya. Rotkovich: On some kinds of completeness in archimedean lattice ordered groups.Funkc. anal. 9 (1977), 138–143. (Russian) |
| Reference:
|
[21] R. Sikorski: Boolean Algebras.Second Edition, Springer-Verlag, Berlin, 1964. Zbl 0123.01303, MR 0126393 |
| Reference:
|
[22] 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 |
| . |
