| Title:
|
Holland’s theorem for pseudo-effect algebras (English) |
| Author:
|
Dvurečenskij, Anatolij |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
47-59 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give two variations of the Holland representation theorem for $\ell $-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $MV$-algebra can be represented as a pseudo-effect algebra or as a pseudo $MV$-algebra of automorphisms of some antilattice or of some linearly ordered set. (English) |
| Keyword:
|
pseudo-effect algebra |
| Keyword:
|
pseudo $MV$-algebra |
| Keyword:
|
antilattice |
| Keyword:
|
prime ideal |
| Keyword:
|
automorphism |
| Keyword:
|
unital po-group |
| Keyword:
|
unital $\ell $-group |
| MSC:
|
03B50 |
| MSC:
|
03G12 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 1164.06329 |
| idMR:
|
MR2206286 |
| . |
| Date available:
|
2009-09-24T11:31:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128053 |
| . |
| Reference:
|
[1] A. Dvurečenskij: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. 72 (2002), 427–445. MR 1902211, 10.1017/S1446788700036806 |
| Reference:
|
[2] A. Dvurečenskij: Ideals of pseudo-effect algebras and their applications.Tatra Mt. Math. Publ. 27 (2003), 45–65. MR 2026641 |
| Reference:
|
[3] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures.Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. MR 1861369 |
| Reference:
|
[4] A. Dvurečenskij, T. Vetterlein: Pseudoeffect algebras. I. Basic properties.Inter. J. Theor. Phys. 40 (2001), 685–701. MR 1831592 |
| Reference:
|
[5] A. Dvurečenskij, T. Vetterlein: Pseudoeffect algebras. II. Group representations.Inter. J. Theor. Phys. 40 (2001), 703–726. MR 1831593 |
| Reference:
|
[6] G. Georgescu, A. Iorgulescu: Pseudo-$MV$ algebras.Multi. Val. Logic 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[7] A. M. W. Glass: Polars and their applications in directed interpolation groups.Trans. Amer. Math. Soc. 166 (1972), 1–25. Zbl 0235.06004, MR 0295991, 10.1090/S0002-9947-1972-0295991-3 |
| Reference:
|
[8] P. Hájek: Observations on non-commutative fuzzy logic.Soft Computing 8 (2003), 38–43. 10.1007/s00500-002-0246-y |
| Reference:
|
[9] C. Holland: The lattice-ordered group of automorphism of an ordered set.Michigan Math. J. 10 (1963), 399–408. Zbl 0116.02102, MR 0158009, 10.1307/mmj/1028998976 |
| . |
