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arXiv · 1006.2557

On the decomposable semigroups and applications

Juan Ignacio García-García·M. Ángeles Moreno-Frías·Alberto Vigneron-Tenorio
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Abstract

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.

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Juan Ignacio García-García, M. Ángeles Moreno-Frías, Alberto Vigneron-Tenorio. 2012-12-18. On the decomposable semigroups and applications. https://doi.org/10.1016/j.jsc.2013.05.009

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