ABSTRACT
A numerical semigroup is a subset S of N (the set of nonnegative integers) closed under addition, 0 ∈ S and H(S) = N \ S is finite. An element x in a numerical semigroup S is a k-factorized element if there exist s1, . . . , sk ∈ S \ {0} such that x = s1 + . . . + sk. The idea of factorization is historically related to Ring Theory. More recently this concept is studied in the more general scope of Semigroup Theory (see for instance [5, 6, 7, 8, 9, 11, 12]).
