论文标题
消失的（CO）Burch及相关子模型的（CO）同源性
Vanishing of (co)homology of Burch and related submodules
论文作者
论文摘要
我们介绍了Burch子模块的概念和弱$ \ Mathfrak M $ -Full模块上的概念，并研究其属性。我们的主要结果之一表明，Burch子模型满足了2个刚性和测试属性。 We also show that over a local ring $(R,\mathfrak m)$ a submodule $M$ of a finitely generated $R$-module $X$, such that either $M=\mathfrak m X$ or $M(\subseteq \mathfrak m X$) is weakly $\mathfrak m$-full in $X$, is 1-Tor rigid and a test module provided that $X$ is faithful (and $ x/m $具有有限的长度，当$ m $弱$ \ mathfrak m $ -full）。作为应用程序，我们提供了一类新的戒指，以使Huneke和Wiegand的猜想对它们具有肯定性。
We introduce the notion of Burch submodules and weakly $\mathfrak m$-full submodules of modules over local rings and study their properties. One of our main results shows that Burch submodules satisfy 2-Tor rigid and test property. We also show that over a local ring $(R,\mathfrak m)$ a submodule $M$ of a finitely generated $R$-module $X$, such that either $M=\mathfrak m X$ or $M(\subseteq \mathfrak m X$) is weakly $\mathfrak m$-full in $X$, is 1-Tor rigid and a test module provided that $X$ is faithful (and $X/M$ has finite length when $M$ is weakly $\mathfrak m$-full). As an application, we give a new class of rings such that a conjecture of Huneke and Wiegand is affirmative over them.
