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Keywords:
half linearly ordered quasigroup; half linearly ordered loop; lexicographic product; isomorphic refinements
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
[6] M. Giraudet and F. Lucas: Groupes à moitié ordonnés. Fund. Math. 139 (1991), 75–89. DOI 10.4064/fm-139-2-75-89 | MR 1150592
[7] J. Jakubík: Lexicographic products of partially ordered groupoids. Czech. Math. J. 14 (1964), 281–305. (Russian) MR 0167558
[8] J. Jakubík: Lexicographic product decompositions of cyclically ordered groups. Czech. Math. J. 48 (1998), 229–241. DOI 10.1023/A:1022881202595 | MR 1624307
[9] J. Jakubík: Lexicographic products of half linearly ordered groups. Czech. Math. J. 51 (2001), 127–138. DOI 10.1023/A:1013761906636 | MR 1814638
[10] A. I. Maltsev: On ordered group. Izv. Akad. Nauk SSSR, Ser. Matem. 13 (1949), 473–482. (Russian)
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