论文标题
三角矩阵环上的淤泥模块
Silting Modules over Triangular Matrix Rings
论文作者
论文摘要
令$λ，γ$为戒指，$ r = \ left（\ begin {array} {cc}λ＆0 \\ m＆γ\ end {array} \ right）$带有$ m $ a $ a $（γ，λ）$ bimodule的三角形矩阵环。令$ x $为正确的$λ$ -MODULE和$ y $ a右$γ$ - 模块。我们证明，$（x，0）$ \ oplus $$（y \otimes_γm，y）$是silting右$ r $ -Module，并且仅当$x_λ$和$y_γ$都是淤积模块和$ y \ y \ y \ y \y_γm$。此外，我们证明，如果$λ$和$γ$在代数封闭的字段上是有限维代数，而$x_λ$和$y_γ$有限地生成，那么$（x，0）$ \ oplus $ $ $y_γ$是支持$τ$ - tilting模块，$ \hom_λ（y \otimes_γm，τx）= 0 $和$ \hom_λ（eλ，y \otimes_γm）= 0 $ with $ e $ the $ e $ themimal iDempotent the maximal iDempotent，以便$ \hom_λ（eλ，x）= 0 $。
Let $Λ,Γ$ be rings and $R=\left(\begin{array}{cc}Λ& 0 \\ M & Γ\end{array}\right)$ the triangular matrix ring with $M$ a $(Γ,Λ)$-bimodule. Let $X$ be a right $Λ$-module and $Y$ a right $Γ$-module. We prove that $(X, 0)$$\oplus$$(Y\otimes_ΓM, Y)$ is a silting right $R$-module if and only if both $X_Λ$ and $Y_Γ$ are silting modules and $Y\otimes_ΓM$ is generated by $X$. Furthermore, we prove that if $Λ$ and $Γ$ are finite dimensional algebras over an algebraically closed field and $X_Λ$ and $Y_Γ$ are finitely generated, then $(X, 0)$$\oplus$$(Y\otimes_ΓM, Y)$ is a support $τ$-tilting $R$-module if and only if both $X_Λ$ and $Y_Γ$ are support $τ$-tilting modules, $\Hom_Λ(Y\otimes_ΓM,τX)=0$ and $\Hom_Λ(eΛ, Y\otimes_ΓM)=0$ with $e$ the maximal idempotent such that $\Hom_Λ(eΛ, X)=0$.
