On the vanishing and non-rigidity of the André-Quillen (co)homology Original Research Article

Let I be an ideal of a commutative ring A and B = A/I. Given n ≥ 2, we characterize the vanishing of the André-Quillen homology modules Hp(A,B, W) for all B-modules W and for all p, 2 ≤ p ≤ n, in terms of some canonical morphisms. As a corollary, we obtain a new proof of a theorem of André. Finally, we construct an example of an ideal I of a commutative ring A such that H2(A,B, W) = 0 and H3(A,B, W) = W for all B-module W.