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

M. Seidali Samani, K. Bahmanpour
2020 Journal of algebraic systems  
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 H^t_I(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 conditions of local cohomology modules, and show that if the Lynch's conjecture, in [11], holds in R[[X]], then it will holds in R.
doi:10.22044/jas.2019.8232.1401 doaj:6be414eeaa264783b3847c35c0138c5a fatcat:nrllunuyr5f6dhcyzv6j4spcru