Lexicographic product decompositions of partially ordered quasigroups (Q2777521)

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.