Title: Approximating Artinian Rings by Gorenstein Rings
Abstract: In this talk, I will make the notion of approximating an Artinian local ring R by Gorenstein Artin local rings precise by introducing a number g(R), associated to R called its Gorenstein colength. The first half deals with the properties of this number which we use to extend results of W. Teter, C. Huneke and A. Vraciu. In particular, we answer the question as to when the Gorenstein colength is two or less. In the second half, we see some natural bounds on the Gorenstein colengths of some special rings and will also compute their Gorenstein colengths by constructing Gorenstein Artin local rings.