ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X]

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper, we calculate the extension of annihilator of local cohomology modules Ht l (M ), t ≥ 0, under the ring extension R ⊂ R[X] (resp., R ⊂ R[[X]]). By using this extension we will present some of the faithfulness con- ditions of local cohomology modules, and show that if the Lynch’s conjecture [11] holds in R[[X]], then it will holds in R.