Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 607-629, 2007

Lexicographic product decompositions of
half linearly ordered loops

Milan Demko

Milan Demko, KM FHPV PU, 17. novembra 1, 081 16 Presov, Slovakia, e-mail: demko@unipo.sk

Abstract: In this paper we prove for an hl-loop $Q$ an assertion analogous to the result of Jakubik 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.

Keywords: half linearly ordered quasigroup, half linearly ordered loop, lexicographic product, isomorphic refinements

Classification (MSC 2000): 20N05, 06F99


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