论文标题
曲线奇点的痕迹理想集
The set of trace ideals of curve singularities
论文作者
论文摘要
本文主要集中于维度一号的局部域。然后，我们获得了一个环的标准，可以根据封闭的理想具有有限数量的痕量理想。我们还探索了与生育扩展，反身理想和反射性Ulrich模块有关的此类环的性质。在非差距四的数值半群环的情况下给出了特别的注意。然后，我们获得了一个环的标准，即具有有限数量的反身理想，直到同构。还探索了纤维产品引起的非域。
This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed ideals. We also explore properties of such rings related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.
