Factorization problems on commutative monoids

An atomic monoid is a commutative monoid in which any nonunit element admits a factorization into irreducible elements. If an atomic monoid is not a uniquely factorization monoid, there are several tools to measure how far the factorizations are to be unique. In this talk we visit some of them. - Sets of lengths of factorizations. - Elasticity of factorizations. - Catenary degree. - Tame degree. We show how these measures can be computed in any finitely generated cancellative commutative monoid, once we know one of its presentations.