论文标题
DG模块结构和最小的免费分辨率模型一个精确的零分量器
DG module structures and minimal free resolutions modulo an exact zero-divisor
论文作者
论文摘要
令$ q $为本地戒指，具有最大理想$ \ mathfrak {n} $，让$ f，g \ in \ mathfrak {n} \ smallSetMinus \ mathfrak {n}^2 $带有$ fg = 0 $。当$ m $是有限的$ q $ -module，$ fm = 0 $时，我们表明，$ m $ $ $ q $的最低免费分辨率在$ q $上面的差异分级模块结构上的差异分级模块结构，而分级为algebra $ q \ langle y，t \ nim t \ mid part \ mid \ partial（y）当$（f，g）$是一对确切的零分配器时，我们使用此结构来描述$ m $ $ $ $ Q/（f）$的最低免费分辨率。
Let $Q$ be a local ring with maximal ideal $\mathfrak{n}$ and let $f,g\in \mathfrak{n}\smallsetminus\mathfrak{n}^2$ with $fg=0$. When $M$ is a finite $Q$-module with $fM=0$, we show that a minimal free resolution of $M$ over $Q$ has a differential graded module structure over the differential graded algebra $Q\langle y,t\mid \partial(y)=f, \partial(t)=gy\rangle$. When $(f,g)$ is a pair of exact zero divisors, we use this structure to describe a minimal free resolution of $M$ over $Q/(f)$.
