Geodesic
Lexicographic product decompositions of half linearly ordered loops
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 607-629.

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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.
Classification : 06F99, 20N05
Keywords: half linearly ordered quasigroup; half linearly ordered loop; lexicographic product; isomorphic refinements 
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     author = {Demko, Milan},
     title = {Lexicographic product decompositions of half linearly ordered loops},
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     pages = {607--629},
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     number = {2},
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     zbl = {1174.06325},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a6/}
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Demko, Milan. Lexicographic product decompositions of half linearly ordered loops. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 607-629. http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a6/