论文标题
部分痕量理想，扭转和规范模块
Partial Trace Ideals, Torsion and Canonical Module
论文作者
论文摘要
对于任何有限生成的模块$ m $，在交换性的一维noetherian本地域中，非零等级，在作者之前的工作“部分跟踪理想和伯格的猜想”中引入并研究了数值不变性$ h（m）$。我们对其建立了一个界限，有助于捕获有关$ m $ $ m $排名一排的扭转子模块的信息，并且在上述上一篇文章中也概括了讨论。在$ m $是规范模块$ω_r$的情况下，我们进一步研究$ h（m）$的范围和属性。反过来，这有助于回答S. Greco的问题，然后提供一些分类。本文中的大多数结果都是基于作者博士学位论文“部分跟踪理想，指挥和伯格的猜想”中提出的结果。
For any finitely generated module $M$ with non-zero rank over a commutative one dimensional Noetherian local domain, the numerical invariant $h(M)$ was introduced and studied in the author's previous work "Partial Trace Ideals and Berger's Conjecture". We establish a bound on it which helps capture information about the torsion submodule of $M$ when $M$ has rank one and it also generalizes the discussion in the mentioned previous article. We further study bounds and properties of $h(M)$ in the case when $M$ is the canonical module $ω_R$. This in turn helps in answering a question of S. Greco and then provide some classifications. Most of the results in this article are based on the results presented in the author's doctoral dissertation "Partial Trace Ideals, The Conductor and Berger's Conjecture".
