Nonnoetherian complete intersections

Michel André
1972 Bulletin of the American Mathematical Society  
Let all rings here be commutative and unitary. As it is well known, a noetherian local ring A (quotient of a regular ring with residue field K) is a complete intersection if and only if the integers ft = dim x Torf (K,19 appear in an equality of formal series of the following type lAx'-a + xr/a-x 2 )'. Furthermore the integer r -s is positive (equal to the dimension of the noetherian ring A). In the nonnoetherian case, by means of André-Quillen homology theory, a criterion is given for
more » ... given for characterizing the local rings for which the integers fi t are defined and appear in an equality of formal series as above. An example shows that there is no relation between the integers r and s in the nonnoetherian case.
doi:10.1090/s0002-9904-1972-13005-2 fatcat:vgr66vqe4zeoxh5x2ko42xddbi