ON THE VANISHING OF THE 2ND ANDRE-QUILLEN (CO)HOMOLOGY FUNCTOR

For a given ideal I of a commutative ring A, B = A/I, the vanishing of the second Andre-Quillen (co)homology functor H-2(A, B, .) is charact erized in terms of the canonical homomorphism alpha : S (I) --> R(I) f rom the symmetric algebra of the ideal I onto its Rees algebra. This i s done by introducing a Koszul complex that characterizes commutative graded algebras which are symmetric algebras.