论文标题
Cohen-Macaulay环和模块的规范学位：调查
Canonical Degrees of Cohen-Macaulay Rings and Modules: a Survey
论文作者
论文摘要
这项调查的目的是讨论接受规范模块的Cohen-Macaulay本地环的不变。与规范理想C相连的每个环R，都有整数 - R的类型，c的降低数 - 提供了有价值的指标，以表达R偏离Gorenstein环的偏差。我们与其他整数（R的根和几个规范学位的根源）扩大了此列表。后者是基于C的REES代数的基于多样性的函数。我们给出了由共同根部产生的三个度的均匀表现。最后，我们尝试将其中一个程度扩展到不一定是理想的环的环。
The aim of this survey is to discuss invariants of Cohen-Macaulay local rings that admit a canonical module. Attached to each such ring R with a canonical ideal C, there are integers--the type of R, the reduction number of C--that provide valuable metrics to express the deviation of R from being a Gorenstein ring. We enlarge this list with other integers--the roots of R and several canonical degrees. The latter are multiplicity based functions of the Rees algebra of C. We give a uniform presentation of three degrees arising from common roots. Finally we experiment with ways to extend one of these degrees to rings where C is not necessarily an ideal.
