On the decomposable semigroups and applications

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.