Structure theorems for certain Gorenstein ideals

Isomorphism Classes of Certain Artinian Gorenstein Algebras

“…Hence we can rephrase the main result in [2] as follows. An ideal I of R is almost stretched and Gorenstein of type (s, t) if and only if it is isomorphic to I a for some a ∈ R.…”

“…Other interesting properties of stretched m-primary ideals can be found in [5]. Sally's result has been considerably extended in [2], where the notion of almost stretched local rings has been introduced. A local Artinian ring (A, m) is said to be almost stretched if the minimal number of generators of m 2 is two.…”

“…In [2] we gave a useful structure theorem for almost stretched Gorenstein local rings in the embedded case, namely when A = R/I with (R, n) a regular local ring of dimension h such that k := R/n is algebraically closed of characteristic 0.…”

A family of local rings with rational Poincaré series

“…Instead, if the square of the maximal ideal of an Artinian reduction is minimally generated by two elements, we say that A is almost stretched. See [11], [9], [5] and [6] for papers concerning these notions.…”

“…We are not developing new methods for the computation of the Betti numbers of the minimal A-free resolution of k; rather we show that the structure theorem we proved in [5] for Artinian almost stretched Gorenstein local rings is very much suitable to the computation of T or…”