2021/05/28 by Jafari, Raheleh, Yaghmaei, Marjan · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2105.13781
We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring \mathbbK[S]. We define the type of S, type, in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when \mathbbK[S] is Cohen-Macaulay. If \mathbbK[S] is a d-dimensional Cohen-Macaulay ring of embedding dimension at most d+2, then type≤ 2. Otherwise, type might be arbitrary large and it has no upper bound in terms of the embedding dimension. Finally, we present a generating set for the conductor of S as an ideal of its normalization.