Rings which are a factor of a Gorenstein ring by its socle

Computing minimal Gorenstein covers

“…Ananthnarayan generalizes some results by Teter [14] and Huneke-Vraciu [10] and provides a characterization of rings of gcl(A) ≤ 2 in terms of the existence of certain self-dual ideals q ∈ A with respect to the canonical module ω A of A satisfying ℓ(A/q) ≤ 2. For more information on this, see [1] or [6,Section 4], for a reinterpretation in terms of inverse systems.…”

“…Proof. If rk C H,v = 1, then all 2-minors of C H,v vanish and, in particular, (14) v l ρ j k − v k ρ j l = 0 for any 1 ≤ k < l ≤ n and 1 ≤ j ≤ h 1 . Recall, from Equation (13), that…”

Rings that are almost Gorenstein

“…Teter's rings [Teter 1974] characterized the Artinian local rings R that are of the form S/(δ), where S is a Gorenstein local Artinian ring and δ generates its socle. We shall prove such rings satisfy condition (A).…”

“…It turns out that Artinian Gorenstein rings modulo their socle are always examples, and this led us to [Teter 1974], which gave an intrinsic characterization of such rings. We are able to improve his result when 2 is a unit, by removing a seemingly important technical assumption of Teter's.…”

Growth in the minimal injective resolution of a local ring

“…Since they have Soc R = m, they belong to (3) and, as will be explained in (3.7), also to (2). Finally, it is a result of Teter [26] that a local ring with m 2 = 0 is Teter. * * * The organization of the paper follows the agenda set by the Main Theorem.…”