THE FINITE BASIS PROBLEM FOR FREE TREE MONOIDS

Abstract

Abstract For each $n\geq 1$ , let $FT_n$ be the free tree monoid of rank n and $E_n$ the full extensive transformation monoid over the finite chain $\{1, 2, \ldots , n\}$ . It is shown that the monoids $FT_n$ and $E_{n+1}$ satisfy the same identities. Therefore, $FT_n$ is finitely based if and only if $n\leq 3$ .