Finite derivation type for semilattices of semigroups

In this paper we investigate how the combinatorial property finite derivation type (FDT) is preserved in a semilattice of semigroups. We prove that if $S= mathcal{S}[Y,S_{alpha}]$ is a semilattice of semigroups such that Y is finite and each S _?? (????Y) has FDT, then S has FDT. As a consequence we can show that a strong semilattice of semigroups $mathcal{S}[Y,S_{alpha},lambda_{alpha,beta}]$ has FDT if and only if Y is finite and every semigroup S _?? (????Y) has FDT.