strong semilattice of semigroups

Malheiro, A. "Finite derivation type for semilattices of semigroups." Semigroup Forum. 84 (2012): 515-526. AbstractWebsite

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_α] is a semilattice of semigroups such that Y is finite and each S_α (α∈Y) has FDT, then S has FDT. As a consequence we can show that a strong semilattice of semigroups S[Y,S_α,λ_{α,β}] has FDT if and only if Y is finite and every semigroup S α (α∈Y) has FDT.