Article
Keywords:
half linearly ordered quasigroup; half linearly ordered loop; lexicographic product; isomorphic refinements
Summary:
In this paper we prove for an hl-loop $Q$ an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop $Q$ with a finite number of lexicographic factors have isomorphic refinements.
References:
[1] V. D. Belousov:
Foundations of the theory of quasigroups and loops. Nauka Moscow, 1967. (Russian)
MR 0218483
[2] Š. Černák:
Lexicographic products of cyclically ordered groups. Math. Slovaca 45 (1995), 29–38.
MR 1335837
[3] M. Demko:
Lexicographic product decompositions of partially ordered quasigroups. Math. Slovaca 51 (2001), 13–24.
MR 1817719 |
Zbl 0986.06012
[4] M. Demko: On half linearly ordered quasigroups. Acta Facultatis Prešov 39 (2002), 39–45.
[5] L. Fuchs:
Partially ordered algebraic systems. Pergamon Press, Oxford-London-New York-Paris, 1963.
MR 0171864 |
Zbl 0137.02001
[7] J. Jakubík:
Lexicographic products of partially ordered groupoids. Czech. Math. J. 14 (1964), 281–305. (Russian)
MR 0167558
[10] A. I. Maltsev: On ordered group. Izv. Akad. Nauk SSSR, Ser. Matem. 13 (1949), 473–482. (Russian)