A formula for the conductor of a semimodule of a numerical semigroup with two generators

Abstract

We provide an expression for the conductor c(Δ) of a semimodule Δ of a numerical semigroup Δ with two generators in terms of the syzygy module of Δ and the generators of the semigroup. In particular, we deduce that the difference between the conductor of the semimodule and the conductor of the semigroup is an element of Γ, as well as a formula for c(Δ) in terms of the dual semimodule of Δ.