In this paper we continue the study of edge-colored graphs associated with finite idempotent algebras initiated in arXiv:2006.09599. We prove stronger connectivity properties of such graphs that will allows us to demonstrate several useful structural features of subdirect products of idempotent algebras such as rectangularity and 2-decomposition.

翻译：本文延续arXiv:2006.09599中关于有限幂等代数相关边着色图的研究。我们证明了此类图更强的连通性性质，这将有助于揭示幂等代数的子直积的几种有用结构特征，如矩形性质和2-分解性质。