论文标题
部分可观测时空混沌系统的无模型预测
Separated monic correspondence of cotorsion pairs and semi-Gorenstein-projective modules
论文作者
论文摘要
给定有限的维数代数$ a $在field $ k $上，还有一个有限的无环颤抖$ q $，让$λ= a \ otimes_k kq/i $，其中$ kq $是$ k $ of $ k $ of $ k $的路径，$ i $ i $ $ $ $是单一的理想。 We show that $(\mathcal X,\mathcal Y)$ is a (complete) hereditary cotorsion pair in $A$-mod if and only if $({\rm smon}(Q,I,\mathcal X), {\rm rep}(Q,I,\mathcal Y))$ is a (complete) hereditary cotorsion pair in $Λ$-mod.我们还表明，只有$λ$，$ a $就会弱戈伦斯坦。前提是$ kq/i $是非偏s的，类别$^{\ perp}λ$ semi-gorenstein-projective $λ$ -Modules与分开的元表示的类别$ {\ rm smon}（q，i，i，i，i，i，i，i，^{\ perp} a）$ if和if的$ ifors $ ifors $ ifors $
Given a finite dimensional algebra $A$ over a field $k$, and a finite acyclic quiver $Q$, let $Λ= A\otimes_k kQ/I$, where $kQ$ is the path algebra of $Q$ over $k$ and $I$ is a monomial ideal. We show that $(\mathcal X,\mathcal Y)$ is a (complete) hereditary cotorsion pair in $A$-mod if and only if $({\rm smon}(Q,I,\mathcal X), {\rm rep}(Q,I,\mathcal Y))$ is a (complete) hereditary cotorsion pair in $Λ$-mod. We also show that $A$ is left weakly Gorenstein if and only if so is $Λ$. Provided that $kQ/I$ is non-semisimple, the category $^{\perp}Λ$ of semi-Gorenstein-projective $Λ$-modules coincides with the category of separated monic representations ${\rm smon}(Q,I,^{\perp}A)$ if and only if $A$ is left weakly Gorenstein.
