#### Document Type

Article

#### Subject Area(s)

Mathematics

#### Abstract

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 nonminimal) DG-algebra resolution of a codimension four almost complete intersection which is produced in [25 and 26].

#### Publication Info

*Transactions of the American Mathematical Society*, Volume 339, Issue 1, 1993, pages 61-85.

© 1983 by American Mathematical Society