  The aim of this work is to reduce the complexity of the available algorithms
for computing the generator sets of a semigroup ideal by using the Hermite
normal form. In order to achieve it we introduce the concept of decomposable
semigroup. If a semigroup is decomposable, the computation of its ideal is
equivalent to compute the ideals of each semigroup in the decomposition, thus
obtaining a reduction of the complexity of the algorithms. Furthermore, since
these computations are mutually independent, they can be carried out in
parallel. The concept of decomposable variety is introduced and a combinatorial
characterization of decomposable semigroup is obtained. Some applications are
also provided.
