On congruences and ideals of partially ordered quasigroups

Milan Demko

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 637-650
  • ISSN: 0011-4642

Abstract

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Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.

How to cite

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Demko, Milan. "On congruences and ideals of partially ordered quasigroups." Czechoslovak Mathematical Journal 58.3 (2008): 637-650. <http://eudml.org/doc/37857>.

@article{Demko2008,
abstract = {Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.},
author = {Demko, Milan},
journal = {Czechoslovak Mathematical Journal},
keywords = {partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal; partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal},
language = {eng},
number = {3},
pages = {637-650},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On congruences and ideals of partially ordered quasigroups},
url = {http://eudml.org/doc/37857},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Demko, Milan
TI - On congruences and ideals of partially ordered quasigroups
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 637
EP - 650
AB - Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.
LA - eng
KW - partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal; partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal
UR - http://eudml.org/doc/37857
ER -

References

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  1. Belousov, V. D., Foundations of the theory of quasigroups and loops, Nauka Moscow (1967), Russian. (1967) MR0218483
  2. Birkhoff, G., Lattice Theory, Amer. Math. Soc., Providence, RI, (1967). (1967) MR0227053
  3. Burris, S., Sankappanavar, A., A Course in Universal Algebra, Springer-Verlag New York, Heidelberg, Berlin (1981). (1981) Zbl0478.08001
  4. Demko, M., Lexicographic product decompositions of partially ordered quasigroups, Math. Slovaca 51 (2001), 13-24. (2001) Zbl0986.06012MR1817719
  5. Fuchs, L., Riesz groups, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 19 (1965), 1-34. (1965) Zbl0125.28703MR0180609
  6. Kiokemeister, F., 10.2307/2371934, Amer. J. Math. 70 (1948), 99-106. (1948) MR0023252DOI10.2307/2371934
  7. Lihová, J., On Riesz groups, Tatra Mt. Math. Publ. 27 (2003), 163-176. (2003) MR2026649
  8. Naik, N., Swammy, B. L. N., Misra, S. S., Lattice ordered commutative loops, Math. Semin. Notes, Kobe Univ. 8 (1980), 57-71. (1980) MR0590165
  9. Naik, N., Swammy, B. L. N., Ideal theory in lattice ordered commutative Moufang loops, Math. Semin. Notes, Kobe Univ. 8 (1980), 443-453. (1980) MR0615863
  10. Testov, V. A., Left-positive Riesz quasigroups. Problems in the theory of webs and quasigroups, 158 (1985), Gos. univ., Kalinin 81-83 Russian. (1985) MR0857474

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