Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal
partially ordered quasigroup; partially ordered loop; Riesz quasigroup; congruence relation; ideal
Summary:
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.
References:
[1] Belousov, V. D.: Foundations of the theory of quasigroups and loops. Nauka Moscow (1967), Russian. MR 0218483
[2] Birkhoff, G.: Lattice Theory, Amer. Math. Soc., Providence, RI. (1967). MR 0227053
[3] Burris, S., Sankappanavar, A.: A Course in Universal Algebra. Springer-Verlag New York, Heidelberg, Berlin (1981). Zbl 0478.08001
[4] Demko, M.: Lexicographic product decompositions of partially ordered quasigroups. Math. Slovaca 51 (2001), 13-24. MR 1817719 | Zbl 0986.06012
[5] Fuchs, L.: Riesz groups. Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 19 (1965), 1-34. MR 0180609 | Zbl 0125.28703
[6] Kiokemeister, F.: A theory of normality for quasigroups. Amer. J. Math. 70 (1948), 99-106. DOI 10.2307/2371934 | MR 0023252
[7] Lihová, J.: On Riesz groups. Tatra Mt. Math. Publ. 27 (2003), 163-176. MR 2026649
[8] Naik, N., Swammy, B. L. N., Misra, S. S.: Lattice ordered commutative loops. Math. Semin. Notes, Kobe Univ. 8 (1980), 57-71. MR 0590165
[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 0615863
[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 0857474
Search
Partner of
