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Lexicographic product decompositions of partially ordered quasigroups. (English) Zbl 0986.06012
Let $$Q$$ be a partially ordered quasigroup with an idempotent element $$h$$. The author defines the notion of the lexicographic product decomposition of $$Q$$ with respect to the element $$h$$. The main result of the paper says that if $$Q=(A_1\circ A_2\circ \dots \circ A_n)_h$$ and $$Q=(B_1\circ B_2\circ \dots \circ B_m)_h$$ are such lexicographic product decompositions and if all factors $$A_i, B_j$$ $$(i=1,\dots , n; j=1,\dots ,m)$$ are directed, then the given lexicographic product decompositions of $$Q$$ have isomorphic refinements.

##### MSC:
 06F15 Ordered groups
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##### References:
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