论文标题
双典型度的概括
Generalization of bi-canonical degrees
论文作者
论文摘要
我们讨论了Cohen-Macaulay本地环的不变式，该戒指承认了一个规范模块$ω$。当$ω$是理想的情况下，每个这样的环r连接在一起时，有整数 - R的类型，$ω$的减少数量 - 提供了有价值的指标，以表达R偏离Gorenstein环的偏差。在ARXIV：1701.05592和ARXIV：1711.09480我们以规范学位和双人态程度扩大了此列表。在这项工作中，我们将双式式学位扩展到$ω$不一定是理想的环。我们还讨论了对无规范模块的戒指的概括，但承认模块共享其某些属性。
We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $ω$. Attached to each such ring R, when $ω$ is an ideal, there are integers--the type of R, the reduction number of $ω$--that provide valuable metrics to express the deviation of R from being a Gorenstein ring. In arXiv:1701.05592 and arXiv:1711.09480 we enlarged this list with the canonical degree and the bi-canonical degree. In this work we extend the bi-canonical degree to rings where $ω$ is not necessarily an ideal. We also discuss generalizations to rings without canonical modules but admitting modules sharing some of their properties.
