PERFECT IDEALS OF GRADE THREE DEFINED BY SKEW-SYMMETRIZABLE MATRICES

Abstract

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type <TEX>${\lambda}$</TEX> > 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 <TEX>$k$</TEX>-algebras R/I, where R is the polynomial ring <TEX>$R=k[v_0,v_1,{\ldots},v_m]$</TEX> over a field <TEX>$k$</TEX> with indeterminates <TEX>$v_i$</TEX> and deg <TEX>$v_i=1$</TEX>.