AI 中文总结
本文针对 Morita 上下文代数，提出一种通过最小逼近与推出交替修正的双边粘合构造，用于生成支撑 $\tau$-倾斜模，并推广了已有准则，通过例子展示了过程的终止性条件。
AI 中文摘要
设 $k$ 是一个域，且设 $\Lambda=\left(\begin{smallmatrix}A&N\M&B\end{smallmatrix}\right)_{\phi,\psi}$ 是一个有限维 Morita 上下文代数。我们引入一种双边逼近构造，该构造通过最小逼近和推出（pushout）交替修正两个角分量，将 $A$ 和 $B$ 上的支撑 $\tau$-倾斜模粘合起来。当这一过程终止时，它产生一个具有指定分量挠类的支撑 $\tau$-倾斜 $\Lambda$-模。单边情形恢复了 Zhang 的三角矩阵构造，而双边相容条件给出直接的角诱导，并且对于取值为根的连接映射，这些条件也是必要的，从而推广了 Gao--Huang 准则。例子表明，即使两个单边相容条件均不满足，双边修正过程也可能终止，而在其他例子中该过程永不终止。
英文摘要
Let $k$ be a field and let $Λ=\left(\begin{smallmatrix}A&N\\M&B\end{smallmatrix}\right)_{ϕ,ψ}$ be a finite-dimensional Morita context algebra. We introduce a bilateral approximation construction which glues support $τ$-tilting modules over $A$ and $B$ by alternately correcting the two corner components through minimal approximations and pushouts. When this process terminates, it yields a support $τ$-tilting $Λ$-module with the prescribed componentwise torsion class. The one-sided case recovers Zhang's triangular-matrix construction, while the two-sided compatibility conditions give direct corner induction and, for radical-valued connecting maps, are also necessary, extending the Gao--Huang criterion. Examples show that the bilateral correction process can terminate even when neither one-sided compatibility condition is satisfied, while in other examples the process never terminates.
Comments24 pages, Comments welcome
