有向图及其路代数

Quivers and Their Path Algebras

本文研究有向图■的几何性质和其路代数K(■)的代数性质之间的关系,给出有向图■的路代数K■是Goldie代数、局部代数、∑-链模代数的充要条件.

Let K(△) denote the path algebra of a quiver △ over a field K. In this paper we study the relationship between the geometric properties of △ and the algebraic properties of K(△). One of the main results of this paper is that the path algebra K(△) is a right ∑-chain module if and only if △ has no loop and there is at most one arrow with any given initial vertex.