1978 HERZOG AND MILLER essary conditions for an algebra to be linked to a complete
intersection. Since these algebras turn out to be hypersurface sections of codimension three …

Structure theorems exist for Gorenstein ideals of small grade. A different parameter one can
use for organizing ideals is deviation (or complete intersection defect). The deviation of the …

We introduce codimension four Gorenstein algebras~(c) for each odd 5 2 3 and D (p) for
each even p 2 4. Each of these algebras is rigid, is in the linkage class of a complete …

A Gorenstein idealK in a local ringR is in the class ℋ if there is a sequence of linked idealsI
0∼ I 1∼⋯∼ I 2n= K withI 0 a complete intersection andI 2i, Gorenstein for alli. IfK is in ℋ …

Let I be a Cohen-Macaulay ideal of grade g> 0 in a local Gorenstein ring (R, m) with residue
class field k. An R-ideal J is said to be linked to I with respect to the regular sequence α …

Let R= $ n> oR, be a noetherian graded ring of Krull dimension d with Ro= k an infinite field,
and R= k [Rl]. The Hilbert function of R is and the Hilbert series is the corresponding …

All rings considered in this paper are noetherian commutative K-algebras, where K is a fixed
field. A ring R is a Gorenstein ring if the injective dimension of R is finite. In a ring R, we say …

Gorenstein rings occur in a multitude of different guises: as rings of invariants, as coordinate
rings of certain determinantal varieties and symmetric semigroup curves, as representatives …

This paper results from an attempt to find all codimension 4 Gorenstein singularities. In [7]
we exploited the idea of linkage by a complete intersection to produce a class of such …

In Chapter 1 we show that when a set D—(Q, P) of generator and relation degrees is given,
Q={q1:..., qu} and P={px,..., pw}, the family GorD of Gorenstein algebras A= R/J with J having …