EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES BAHMANPOUR, KAMAL;
Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if () be a sub-set of a system of parameters for M, then the R-module (R) is faithful, i.e., Ann (R) = 0. Also, it is shown that, if (R) = 0 for all i > dim R - dim R/I, then the R-module is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in . Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module , when for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra is a flat R-algebra.