论文标题
独立序列和弗雷尼斯标准
Independent sequences and freeness criteria
论文作者
论文摘要
让$ m $成为Noetherian Local Ring $ a $的模块。我们从Lech和Hanes的意义上研究了$ \ Mathfrak {m} _a $的元素元素的$ m $独立序列。主要工具是根据相关的Koszul复合物的序列独立的新表征。作为应用程序，我们为链接理论提供了结果，在存在强烈的$ m $ m $的长度序列$ edim（a）$（a）$（a）$的情况下，是$ m $的freeness标准，以及来自Calegari和Geraghty的修补方法的另一个FreeNess Criterion在其2018 Paper中的Balancated模块中启发。
Let $M$ be a module over a Noetherian local ring $A$. We study $M$-independent sequences of elements of $\mathfrak{m}_A$ in the sense of Lech and Hanes. The main tool is a new characterization of the $M$-independence of a sequence in terms of the associated Koszul complex. As applications, we give a result in linkage theory, a freeness criterion for $M$ in terms of the existence of a strongly $M$-independent sequence of length $edim(A)$, and another freeness criterion inspired from the patching method of Calegari and Geraghty for balanced modules in their 2018 paper.
