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Type and conductor of simplicial affine semigroups
Journal of Pure and Applied Algebra ( IF 0.7 ) Pub Date : 2021-07-21 , DOI: 10.1016/j.jpaa.2021.106844
Raheleh Jafari 1 , Marjan Yaghmaei 2
Affiliation  

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 K[S]. We define the type of S, 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 K[S] is Cohen-Macaulay. If K[S] is a d-dimensional Cohen-Macaulay ring of embedding dimension at most d+2, then type(S)2. Otherwise, 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.



中文翻译:

单纯仿射半群的类型和导体

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[]. 我们定义S的类型,类型(),就S的一些 Apéry 集而言,并表明它与半群环的 Cohen-Macaulay 型重合,当[]是科恩-麦考利。如果[]是最多嵌入维数的d维 Cohen-Macaulay 环d+2, 然后 类型()2. 否则,类型()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。

更新日期:2021-07-26
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