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 $\mathbb{K}[S]$. We define the type of S, $\mathrm{type}(S)$, in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when $\mathbb{K}[S]$ is Cohen-Macaulay. If $\mathbb{K}[S]$ is a d-dimensional Cohen-Macaulay ring of embedding dimension at most $d+2$, then $\mathrm{type}(S)\le 2$. Otherwise, $\mathrm{type}(S)$ 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.

我们将数值半群的伪 Frobenius 数推广到单纯仿射半群的上下文中。这样，我们刻画了单纯仿射半群环的 Cohen-Macaulay 型$\mathbb{钾}[秒]$. 我们定义S的类型，$\mathrm{类型}(秒)$，就S的一些 Apéry 集而言，并表明它与半群环的 Cohen-Macaulay 型重合，当$\mathbb{钾}[秒]$是科恩-麦考利。如果$\mathbb{钾}[秒]$是最多嵌入维数的d维 Cohen-Macaulay 环$d+2$， 然后 $\mathrm{类型}(秒)\le 2$. 否则，$\mathrm{类型}(秒)$可能是任意大的，并且在嵌入维度方面没有上限。最后，我们提出了S的导体的生成集作为其归一化的理想。