ON THE VANISHING AND NONRIGIDITY OF THE ANDRE-QUILLEN (CO)HOMOLOGY

Let I be an ideal of a commutative ring A and B = A/I. Given n greater than or equal to 2, we characterize the vanishing of the Andre-Quille n homology modules H-p(A, B, W) for all B-modules W and for all p, 2 l ess than or equal to p less than or equal to n, in terms of some canon ical morphisms. As a corollary, we obtain a new proof of a theorem of Andre. Finally, we construct an example of an ideal I of a commutative ring A such that H-2(A, B, W) = 0 and H-3(A, B, W) = W for all B-modu le W. (C) 1997 Elsevier Science B.V.