An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation

Abstract

In 1949 M.~Sholander proved that every medial cancellation groupoid can be embedded into a medial quasigroup. In this paper we prove that it is also true for $n$-ary cancellation groupoids, namely, every medial cancellation $n$-ary groupoid can be embedded into a medial $n$-ary quasigroup.