GENERAL SYMBOLIC POWERS - A HOMOLOGICAL POINT-OF-VIEW

Let I be an ideal of a Noetherian ring R and let S be a multiplicative ly closed subset of R. We define the n-th (S)-symbolic power of I as S (I-n) = I-n R(S) boolean AND R. The purpose of this paper is to compar e the topologies defined by the adic {I-n}(n greater than or equal to 0) and the (S)-symbolic filtration {S(I-n)}(n greater than or equal to 0) using the direct system {Exdt(R)(i)(R/I-n,R)}(n greater than or eq ual to 0).