Geodesic
On congruences and ideals of partially ordered quasigroups
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 637-650
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 06F99, 20N05
Keywords: partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal 
@article{CMJ_2008_58_3_a3,
     author = {Demko, Milan},
     title = {On congruences and ideals of partially ordered quasigroups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {637--650},
     year = {2008},
     volume = {58},
     number = {3},
     mrnumber = {2455927},
     zbl = {1174.06326},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a3/}
}
TY  - JOUR
AU  - Demko, Milan
TI  - On congruences and ideals of partially ordered quasigroups
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 637
EP  - 650
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a3/
LA  - en
ID  - CMJ_2008_58_3_a3
ER  - 
%0 Journal Article
%A Demko, Milan
%T On congruences and ideals of partially ordered quasigroups
%J Czechoslovak Mathematical Journal
%D 2008
%P 637-650
%V 58
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a3/
%G en
%F CMJ_2008_58_3_a3
Demko, Milan. On congruences and ideals of partially ordered quasigroups. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 637-650. http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a3/

[1] Belousov, V. D.: Foundations of the theory of quasigroups and loops. Nauka Moscow (1967), Russian. | MR

[2] Birkhoff, G.: Lattice Theory, Amer. Math. Soc., Providence, RI. (1967). | MR

[3] Burris, S., Sankappanavar, A.: A Course in Universal Algebra. Springer-Verlag New York, Heidelberg, Berlin (1981). | Zbl

[4] Demko, M.: Lexicographic product decompositions of partially ordered quasigroups. Math. Slovaca 51 (2001), 13-24. | MR | Zbl

[5] Fuchs, L.: Riesz groups. Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 19 (1965), 1-34. | MR | Zbl

[6] Kiokemeister, F.: A theory of normality for quasigroups. Amer. J. Math. 70 (1948), 99-106. | DOI | MR

[7] Lihová, J.: On Riesz groups. Tatra Mt. Math. Publ. 27 (2003), 163-176. | MR

[8] Naik, N., Swammy, B. L. N., Misra, S. S.: Lattice ordered commutative loops. Math. Semin. Notes, Kobe Univ. 8 (1980), 57-71. | MR

[9] Naik, N., Swammy, B. L. N.: Ideal theory in lattice ordered commutative Moufang loops. Math. Semin. Notes, Kobe Univ. 8 (1980), 443-453. | MR

[10] Testov, V. A.: Left-positive Riesz quasigroups. Problems in the theory of webs and quasigroups. 158 (1985), Gos. univ., Kalinin 81-83 Russian. | MR