engleski

A note on medial quasigroups

In this short note we prove two results about medial quasigroups. First, let phi and psi be binary operations defined by multiplication, left and right division in a medial quasigroup. Then phi and psi are mutually medial, i.e. phi(psi(a, b), psi(c, d)) = psi(phi(a, c), phi(b, d)). Second, four points a, b, c, d in an idempotent medial quasigroup form a parallelogram if and only if d=(a/b)(b\c).

medial quasigroup ; parallelogram

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