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Canonical bases of modules over one dimensional \(\mathbf{K}\)-algebras

  • A. Abbas
  • A. AssiEmail author
  • P. A. García-Sánchez
Original Paper
  • 40 Downloads

Abstract

Let \({\mathbf {K}}\) be a field and denote by \({\mathbf {K}}[t]\), the polynomial ring with coefficients in \({\mathbf {K}}\). Set \(\mathbf A={\mathbf {K}}[f_1,\ldots ,f_s]\), with \(f_1,\ldots , f_s \in \mathbf K[t]\). We give a procedure to calculate the monoid of degrees of the \({\mathbf {K}}\) algebra \({\mathbf {M}}=F_1{\mathbf {A}}+\cdots +F_r{\mathbf {A}}\) with \(F_1,\ldots , F_r\in {\mathbf {K}}[t]\). We show some applications to the problem of the classification of plane polynomial curves (that is, plane algebraic curves parametrized by polynomials) with respect to some of their invariants, using the module of Kähler differentials.

Keywords

Numerical semigroups Canonical bases Polynomial curves Kähler differentials 

Mathematics Subject Classification

14H20 14H50 05E15 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.MathématiquesUniversité d’AngersAngers ceded 01France
  2. 2.Departamento de Álgebra and IEMath-GRUniversidad de GranadaGranadaSpain

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