Perfect Ideals of Grade Three Defined by Skew-Symmetrizable Matrices

Abstract

Abstract. Brown provided a structure theorem for a class of perfect ideals of grade 3 with type 2 and λ > 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 , . . . , vm] over a field k with indeterminates v i and deg v i = 1.

On a Class of Gorenstein Ideals of Grade Four

“…In [6], let r be an odd integer with r > 1, s be a regular element, A be a r × 4 matrix and U be a 4 × 4 alternating matrix. We define an (r + 4) × (r + 4) skew-symmetrizable matrix G 3 by…”