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Recent research of the author has given an explicit geometric description offree (two-sided) adequate semigroups and monoids, as sets of labelled directedtrees under a natural combinatorial multiplication. In this paper we show thatthere are natural embeddings of each free right adequate and free left adequatesemigroup or monoid into the corresponding free adequate semigroup or monoid.The corresponding classes of trees are easily described and the resultinggeometric representation of free left adequate and free right adequatesemigroups is even easier to understand than that in the two-sided case. We useit to establish some basic structural properties of free left and rightadequate semigroups and monoids.

Free left and right adequate semigroups