摘要
Let R = k[x1,...,xn], where k is a field. The path ideal （of length t ≥ 2） of a directed graph G is the monomial ideal], denoted by It （G）, whose generators correspond to the directed paths of length t in G. Let F be a directed rooted tree. We characterize all such trees whose path ideals are unmixed and Cohen-Macaulay. Moreover, we show that R/It（F） is Corenstein if and only if the Stanley-Reisner simplicial complex of It（Г） is a matroid.
Let R = k[x1,...,xn], where k is a field. The path ideal （of length t ≥ 2） of a directed graph G is the monomial ideal], denoted by It （G）, whose generators correspond to the directed paths of length t in G. Let F be a directed rooted tree. We characterize all such trees whose path ideals are unmixed and Cohen-Macaulay. Moreover, we show that R/It（F） is Corenstein if and only if the Stanley-Reisner simplicial complex of It（Г） is a matroid.
