Alberich-Carramiñana, MaríaAlmirón, PatricioMoyano-Fernández, Julio-José2023-06-172023-06-172021-05https://hdl.handle.net/20.500.14352/7198In this paper we characterize the value set ∆ of the R-modules of the form R+zR for the local ring R associated to a germ ξ of an irreducible plane curve singularity with one Puiseux pair. In the particular case of the module of Kähler differentials attached to ξ , we recover some results of Delorme. From our characterization of ∆ we introduce a proper subset of semimodules over the value semigroup of the ring R. Moreover, we provide a geometric algorithm to construct all possible semimodules in this subset for a given value semigroup.engjournal articleopen access512.7R-modulesΓ-semimodulesCurve singularitiesModuliValue setsÁlgebraGeometria algebraicaGrupos (Matemáticas)1201 Álgebra1201.01 Geometría Algebraica