On the annihilators and attached primes of top local cohomology modules

Let be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that , where is the largest submodule of M such that . Several applications of this result are given. Among other things, it is shown that there exists an ideal of R such that . Using this, we show that if , then These generalize the main results of Bahmanpour et al. (see [2, Theorem 2.6]), Hellus (see [7, Theorem 2.3]), and Lynch (see [10, Theorem 2.4]).