On the Calculation of gl.dim Gℕ(A) and ${\rm gl.dim}\, \widetilde{A}$ by Using Gröbner Bases

Abstract

Let [Formula: see text] be a K-algebra defined by a finite Gröbner basis [Formula: see text]. In this paper, it is shown how to use the Ufnarovski graph [Formula: see text] and the graph of n-chains [Formula: see text] to calculate gl.dim Gℕ(A) and [Formula: see text], where Gℕ(A), respectively [Formula: see text], is the associated ℕ-graded algebra of A, respectively the Rees algebra of A with respect to the ℕ-filtration FA of A induced by a weight ℕ-grading filtration of K 〈X1,…, Xn〉.