Title:
|
Products of partially ordered quasigroups (English) |
Author:
|
Demko, Milan |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
49 |
Issue:
|
2 |
Year:
|
2008 |
Pages:
|
209-217 |
. |
Category:
|
math |
. |
Summary:
|
We describe necessary and sufficient conditions for a direct product and a lexicographic product of partially ordered quasigroups to be a positive quasigroup. Analogous questions for Riesz quasigroups are studied. (English) |
Keyword:
|
partially ordered quasigroup |
Keyword:
|
positive quasigroup |
Keyword:
|
Riesz quasigroup |
Keyword:
|
direct product |
Keyword:
|
lexicographic pro\-duct |
MSC:
|
06F05 |
MSC:
|
06F99 |
MSC:
|
20N05 |
idZBL:
|
Zbl 1212.06033 |
idMR:
|
MR2426886 |
. |
Date available:
|
2009-05-05T17:07:39Z |
Last updated:
|
2013-09-22 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119716 |
. |
Reference:
|
[1] Bosbach B.: Lattice ordered binary systems.Acta. Sci. Math. 32 (1988), 257-289. MR 0980278 |
Reference:
|
[2] Bruck R.H.: A Survey of Binary Systems.Ergebnisse der Mathematik, Neue Folge, Heft 20, Springer, Berlin, 1958. Zbl 0141.01401, MR 0093552 |
Reference:
|
[3] Evans T.: Lattice-ordered loops and quasigroups.J. Algebra 16 (1970), 218-226. MR 0263714, 10.1016/0021-8693(70)90026-8 |
Reference:
|
[4] Hartman P.A.: Integrally closed and complete ordered quasigroups and loops.Proc. Amer. Math. Soc. 33 (1972), 250-256. MR 0295985, 10.1090/S0002-9939-1972-0295985-3 |
Reference:
|
[5] Kalhoff F.B., Priess-Crampe S.H.G.: Ordered loops and ordered planar ternary rings.Quasigroups and loops: theory and applications, Sigma Ser. Pure Math. 8, Heldermann, Berlin, 1990, pp.445-465. MR 1125820 |
Reference:
|
[6] Lihová J.: On Riesz groups.Tatra Mt. Math. Publ. 27 (2003), 163-176. Zbl 1065.06016, MR 2026649 |
Reference:
|
[7] Tararin V.M.: Ordered quasigroups.Izv. Vyssh. Uchebn. Zaved. Mat. 1 (1979), 82-86 (in Russian). MR 0541491 |
Reference:
|
[8] Testov V.A.: Left-positive quasigroups with a lattice order.Webs and quasigroups (in Russian), 153, pp.110-114, Kalinin. Gos. Univ., Kalinin, 1982. MR 0674313 |
Reference:
|
[9] Testov V.A.: Left-positive Riesz quasigroups.Problems in the theory of webs and quasigroups (in Russian), 158, pp.81-83, Kalinin. Gos. Univ., Kalinin, 1985. MR 0857474 |
Reference:
|
[10] Zelinsky D.: Nonassociative valuations.Bull. Amer. Math. Soc. 54 (1948), 175-183. MR 0023815, 10.1090/S0002-9904-1948-08980-7 |
Reference:
|
[11] Zelinsky D.: On ordered loops.Amer. J. Math. 70 (1948), 681-697. MR 0027001, 10.2307/2372206 |
. |