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Classification Of The Tor-Algebras Of Codimension Four Almost Complete Intersections, Andrew R. Kustin

Faculty Publications

Let (R, m, k) be a local ring in which 2 is a unit. Assume that every element of k has a square root in k . We classify the algebras Tor'(R/J, k) as J varies over all grade four almost complete intersection ideals in R. The analogous classification has already been found when J varies over all grade four Gorenstein ideals [21], and when J varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebraso f codimension four Gorenstein rings, as well as the (usually …