Finitistic dimension of monomial algebras. (Q1399175)

The author describes the minimal projective resolution of the left ideal generated by any monomial \(p\) in a monomial algebra in terms of a combinatorial object, which is called the dimension tree of \(p\); and presents two algorithms for computing this dimension tree. As an application the author obtains an effective way to compute the finitistic dimension for monomial algebras. Finally, the author proposes some necessary and sufficient conditions for a monomial algebra to have the finitistic dimension at most \(1\).