Products of partially ordered quasigroups

Milan Demko

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 2, page 209-217
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Demko, Milan. "Products of partially ordered quasigroups." Commentationes Mathematicae Universitatis Carolinae 49.2 (2008): 209-217. <http://eudml.org/doc/250447>.

@article{Demko2008,
abstract = {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.},
author = {Demko, Milan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {partially ordered quasigroup; positive quasigroup; Riesz quasigroup; direct product; lexicographic product; partially ordered quasigroup; positive quasigroup; Riesz quasigroup; direct product; lexicographic product},
language = {eng},
number = {2},
pages = {209-217},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products of partially ordered quasigroups},
url = {http://eudml.org/doc/250447},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Demko, Milan
TI - Products of partially ordered quasigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 209
EP - 217
AB - 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.
LA - eng
KW - partially ordered quasigroup; positive quasigroup; Riesz quasigroup; direct product; lexicographic product; partially ordered quasigroup; positive quasigroup; Riesz quasigroup; direct product; lexicographic product
UR - http://eudml.org/doc/250447
ER -

References

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  2. Bruck R.H., A Survey of Binary Systems, Ergebnisse der Mathematik, Neue Folge, Heft 20, Springer, Berlin, 1958. Zbl0141.01401MR0093552
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  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. MR1125820
  6. Lihová J., On Riesz groups, Tatra Mt. Math. Publ. 27 (2003), 163-176. (2003) Zbl1065.06016MR2026649
  7. Tararin V.M., Ordered quasigroups, Izv. Vyssh. Uchebn. Zaved. Mat. 1 (1979), 82-86 (in Russian). (1979) MR0541491
  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. MR0674313
  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. MR0857474
  10. Zelinsky D., 10.1090/S0002-9904-1948-08980-7, Bull. Amer. Math. Soc. 54 (1948), 175-183. (1948) MR0023815DOI10.1090/S0002-9904-1948-08980-7
  11. Zelinsky D., 10.2307/2372206, Amer. J. Math. 70 (1948), 681-697. (1948) MR0027001DOI10.2307/2372206

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