Given surjective homomorphisms R→ T← S of local rings, and ideals in R and S that are
isomorphic to some T-module V, the connected sum R⋕ TS is defined to be the ring …

Let R be a commutative noetherian local ring with residue field k and assume that it is not
Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue …

We introduce classes of rings that are close to being Gorenstein and prove they arise
naturally as specializations of rings of countable CM type. We study these rings in detail and …

Journal of Algebra The Gorenstein colength of an Artinian local ring Page 1 Journal of Algebra
320 (2008) 3438–3446 Contents lists available at ScienceDirect Journal of Algebra …

Let R be a Cohen–Macaulay local ring possessing a canonical module. In this paper, we
consider when the maximal ideal of R is self-dual—ie, it is isomorphic to its canonical dual …

Let R be a Cohen–Macaulay local K-algebra or a standard graded K-algebra over a field K
with a canonical module. The trace of is the ideal of R which is the sum of those ideals with …

We give a new characterization, in the equicharacteristic case, of Teter rings by using
Macaulay inverse systems. We extend the previous characterizations due to Teter, to …

We compute the canonical trace of generic determinantal rings and provide a sufficient
condition for the trace to specialize. As an application, we determine the canonical trace\(tr …

The aim of this paper is to extend the characterization of Teter rings of [9] to Artin rings of
Gorenstein colength two and to improve and complete the result [1, Theorem 5.5] on such …

As is known, for isolated hypersurface singularities and complete intersections of positive
dimension, the Milnor number is the least upper bound for the Tjurina number, ie,. In this …