Finite derivation type for large ideals

In this paper we give a partial answer to the following question: does a large subsemigroup of a semigroup S with the finite combinatorial property finite derivation type ( FDT ) also have the same property? A positive answer is given for large ideals. As a consequence of this statement we prove that, given a finitely presented Rees matrix semigroup M [ S ; I , J ; P ], the semigroup S has FDT if and only if so does M [ S ; I , J ; P ].