The main goal of the paper is to establish a sufficient condition for a two-valenced association scheme to be schurian and separable. To this end, an analog of the Desargues theorem is introduced for a noncommutative geometry defined by the scheme in question. It turns out that if the geometry has enough many Desarguesian configurations, then under a technical condition, the scheme is schurian and separable. This result enables us to give short proofs for known statements on the schurity and separability of quasi-thin and pseudocyclic schemes. Moreover, by the same technique, we prove a new result: given a prime p, any \(\{1,p\}\)-scheme with thin residue isomorphic to an elementary abelian p-group of rank greater than two, is schurian and separable.

本文的主要目的是为两价关联方案建立舒克尔式和可分离性的充分条件。为此，针对由所讨论的方案定义的非可交换几何引入了Desargues定理的类似物。事实证明，如果几何图形具有足够多的Desarguesian构型，则在技术条件下，该方案是schurian且可分离的。这一结果使我们能够为拟稀疏和伪循环方案的扰动和可分离性的已知陈述提供简短证明。此外，通过相同的技术，我们证明了一个新的结果：给定素数 p，任何具有稀有残基同构基本abelian p-群且秩大于2的\（\ {1，p \} \）-方案都是学者和可分离。