algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety numerical semigroups; irreducible numerical semigroups; free numerical semigroups; semigroups associated with irreducible meromorphic series; Newton-Puiseux exponents; characteristic sequences; intersection multiplicity; minimal presentations; factorizations; non-unique factorization; Feng-Rao distance 