Properties of the resolutions of almost Gorenstein algebras

Abstract

We study properties of the resolution of almost Gorenstein artinian algebras R / I , i.e. algebras defined by ideals I such that I = J + ( f ) , with J Gorenstein ideal and f ∈ R . Such algebras generalize the well known almost complete intersection artinian algebras. Then we give a new explicit description of the resolution and of the graded Betti numbers of almost complete intersection ideals of codimension 3 and we characterize the ideals whose graded Betti numbers can be achieved using artinian monomial ideals.