On decomposable semigroups and applications

In this work we develop a framework to decrease the time complexity of well-known algorithms to compute the generator sets of a semigroup ideal by using the Hermite normal form. We introduce idea of decomposable semigroups, which fulfills that the computation of its ideal can be achieved by separately calculating over smaller semigroups, products of the decomposition. Our approach does not only decrease the time complexity of the problem, but also allows using parallel computational techniques. A combinatorial characterization of these semigroups is obtained and the concept of decomposable variety is introduced. Finally, some applications and practical results are provided.