How to check if a finitely generated commutative monoid is a principal ideal commutative monoid

  • Authors:

  • José Carlos Rosales;Pedro A. García-Sánchez;Juan Ignacio García-García

  • Affiliations:

  • Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain;Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain;Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain

  • Venue:
  • ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
  • Year:
  • 2000

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Abstract

We give a characterization of commutative monoids satisfying that all its ideals are principal. Using this characterization we construct an algorithm for deciding whether a finitely generated commutative monoid satisfies this condition.