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 = S[Y; S_y] is a semilattice of semigroups such that Y is finite and each S_y(y in Y ) has FDT, then S has FDT. As a consequence we can show that a strong semilattice of semigroups S[Y; S_y; ¸\phi_¯] has FDT if and only if Y is finite and every semigroup S_y (y in Y ) has FDT.