Abstract

We present an explicit minimal set of generators for the defining ideal of the family of Backelin semigroups and find its Betti numbers. In particular, we compute the type of the semigroup as well, correcting a claim in the literature. Additionally, we show that the Betti numbers of the corresponding numerical semigroup ring coincide to those of its tangent cone.

中文翻译：

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Backelin 半群的生成元、关系和类型

摘要

我们为 Backelin 半群族的定义理想提出了一个显式的最小生成器集，并找到了它的 Betti 数。特别是，我们还计算了半群的类型，纠正了文献中的说法。此外，我们证明了相应数值半群环的 Betti 数与其切锥的 Betti 数重合。