论文标题
半群环中单一理想的标准对
Standard pairs for monomial ideals in semigroup rings
论文作者
论文摘要
我们将标准对的概念扩展到了半群环中单一理想的背景。标准对可以用作数据结构，以编码这种单项理想，为生成非常适合计算交集，分解和多重性的替代方案。我们提供算法来计算产生集的标准对，反之亦然，并使我们的所有结果有效。我们假设下面的半群环是积极分级的，但不一定是正常的。缺乏正常性是这项工作中大多数挑战，微妙和创新的根源。
We extend the notion of standard pairs to the context of monomial ideals in semigroup rings. Standard pairs can be used as a data structure to encode such monomial ideals, providing an alternative to generating sets that is well suited to computing intersections, decompositions, and multiplicities. We give algorithms to compute standard pairs from generating sets and vice versa and make all of our results effective. We assume that the underlying semigroup ring is positively graded, but not necessarily normal. The lack of normality is at the root of most challenges, subtleties, and innovations in this work.
