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引用次数: 0
摘要
本注释的目的是证明在 k 为域的\(S=k[x_1,\ldots ,x_n]\)上有限生成的有级模块 M、当且仅当它的算术度 \({\text{adeg}}(M)\)与 \({\text {adeg}}(F/{text {gin}}_\textrm{revlex}(U))\) 一致时，它才是科恩-麦考莱序列，其中 F 是一个有级自由 S 模块，并且 \(M \cong F/U\).这正面回答了 Lu 和 Yu 在 2016 年提出的猜想。
The purpose of this note is to show that a finitely generated graded module M over \(S=k[x_1,\ldots ,x_n]\), k a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree \({\text {adeg}}(M)\) agrees with \({\text {adeg}}(F/{\text {gin}}_\textrm{revlex}(U))\), where F is a graded free S-module and \(M \cong F/U\). This answers positively a conjecture of Lu and Yu from 2016.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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