  In this paper we introduce the notion of m-irreducibility that extends the
standard concept of irreducibility of a numerical semigroup when the
multiplicity is fixed. We analyze the structure of the set of m-irreducible
numerical semigroups, we give some properties of these numerical semigroups and
we present algorithms to compute the decomposition of a numerical semigroups
with multiplicity m into m-irreducible numerical semigroups.
