On the attached primes of top local cohomology modules.

Let a be an ideal of Noetherian ring R and M a finitely generated R-module such that cd (a , M) = c . In this paper, we investigate Att R (H a c (M)) . Among other things, it is shown that Max { p ∈ Supp R M | cd (a , R / p) = c } ⊆ Att R (H a c (M)) . We also show that Att R (H a c (M)) = { p ∈ Supp R M | cd (a , R / p) = c , p = Ann R (H a c (R / p)) } and { p ∈ Supp R M | cd (a , R / p) = c , dim R / p − 1 ≤ cd (a , R / p) ≤ dim R / p } ⊆ Att R (H a c (M)). Finally, we prove that if (R , m) is a local ring and dim R / a = 1 then Att R (H a c (M)) = { p ∈ Supp R M | cd (a , R / p) = cd (a , M) } . Then by using this, it is shown that if (R , m) is a local ring then { p ∈ Supp R M | cd (a , R / p) = c , dim R / (a + p) = 1 } ⊆ Att R (H a c (M)). [ABSTRACT FROM AUTHOR]