Bulletin of the
Korean Mathematical Society BKMS

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type 2 and $\lambda >0.$ We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals $I$ of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras $R/I,$ where $R$ is the polynomial ring $R=k[v_0, v_1, \ldots, v_m]$ over a field $k$ with indeterminates $v_i$ and $\deg v_i=1.$

Keywords: almost complete intersection of grade 3, perfect ideal of grade 3, minimal free resolution, linkage

MSC numbers: 13C05, 13H10, 13C02, 13C40