倾斜代数和预投射分支中模的一些性质

Tilted Algebra and Properties of Modules in Preprojective Components

证明了倾斜代数含有一个连接分支Γ,并且在这一分支中,从内射模到投射模的路(若有)都是截口路.还证明了预投射分支中模的既约前趋的个数是有限的,且有rad∞(·,X)=0,其中X为此分支中的模.

We prove that tilted algebra has a connecting component and the path(if exist) from injective module to projective module is sectional in the component. At the same time, the set of irreducible predecessors of module in preprojective components is finite and rad∞(·,X)=0.