Numerical semigroups and aplications

Cofinanciado por:
Project title | Numerical semigroups and aplications
Project Code | PTDC/MAT/73544/2006
Main objective |

Region of intervention |

Beneficiary entity | Universidade de Évora(líder)

Approval date | 06-06-2007
Start date | 01-09-2007
Date of the conclusion | 31-08-2010

Total eligible cost |
European Union financial support |
National/regional public financial support |
Apoio financeiro atribuído à Universidade de Évora | 20000 €

Summary

The project is divided in the tasks, each one divided in several subtasks:

1. Given a subset X of N de set N - X is not necessarily a numerical semigroup, our purpose is precisely to characterize those finite subsets of N wich are gap sets for a numerical semigroup.

2. Study and improvement of the invariants of numerical semigroups.

a. Study of the invariants related to Med-semigroups, Arf semigroups and Saturated semigroups.

 b. Implementation of the newly obtained results.

3. Let ( u_1, u_2 , … ) be an increasing succession in N. To determine the succession of numerical semigroups generated by {u_1 , …}, {u_2 ,u_3 , ….}. To know if the properties of the semigroups we obtain depend of the given initial succession.

4. Study semigroups associates the classes of projected in C* - algebras. These semigroups generate the groups of K-theory K_0 de C*- algebras.


Goals, activities and expected/achieved results

To develop high quality scientific research in the area of numerical semigroups and their relations and aplications with the other areas of mathematics and the algorithms related to it.
To promote contacts and cooperation with other international research teams throw the realization of some joint seminars, missions abroad and an international conference dedicated to the subject.
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