Betti numbers and almost complete intersection monomial ideals

Let R=K[x₁,…, xₙ] be the polynomial ring in n variables over a field K and let I be a monomial ideal of R. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.