%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T The minimal system of generators of an affine, plane and normal semigroup
%D 2024
%@ 1846-579X
%U http://hdl.handle.net/10498/35413
%X If X is a nonempty subset of Qk , the cone generated by X is C(X) = {q1x1 +
· · ·+qnxn | n ∈ N\{0},{q1, . . . ,qn} ⊆ Q+0 and {x1, . . . ,xn} ⊆ X}. In this work we present an
algorithm which calculates from {(a1,b1), (a2,b2)} ⊆ N2 , the minimal system of generators
of the affine semigroup C({(a1,b1), (a2,b2)}) ∩N2. This algorithm is based on the study of
proportionally modular Diophantine inequalities carried out in [1]. Also, we present an upper
bound for the embedding dimension of this semigroup.
%K Affine semigroup
%K Bézout sequence
%K normal semigroup
%K plane semigroup
%K triangulation
%K embedding dimension
%~ Universidad de Cádiz