Annihilators of Local Cohomology Modules

Let (R, 𝔪) be a commutative Noetherian complete local ring, M a nonzero finitely generated R-module of dimension n, and I be an ideal of R. In this paper we calculate the annihilator of the top local cohomology module . Also, if (R, 𝔪) is a Noetherian local Cohen–Macaulay ring of dimension d and I is a nonzero proper ideal of R, then we calculate the annihilator of the first nonzero local cohomology module . Finally, we show that if R is an arbitrary Noetherian ring, I an ideal of R, and M is a nonzero finitely generated R-module with cd(I, M) = t ≥ 0, then there exists a submodule N of M such that . This is a generalization of the main result of Bahmanpour, A'zami, and Ghasemi [1 Bahmanpour , K. , A'zami , J. , Ghasemi , G. ( 2012 ). On the annihilators of local cohomology modules . J. Algebra 363 : 8 – 13 .[Crossref], [Web of Science ®] , [Google Scholar]] for all ideals of an arbitrary Noetherian ring R.