On top local cohomology modules, Matlis duality and tensor products.

Let 𝔞 be an ideal of a local ring (R , 𝔪) with c = cd (𝔞 , R) the cohomological dimension of 𝔞 in R. In the case that c = dim R , we first give a bound for depth D (H 𝔞 c (R)) , where c > 2 and (R , 𝔪) is complete. Later, H 𝔞 c (R) ⊗ R H 𝔞 c (R) , D (H 𝔞 c (R)) ⊗ R D (H 𝔞 c (R)) and H 𝔞 c (R) ⊗ R D (H 𝔞 c (R)) are examined. In the case c = dim R − 1 , the set Att R H 𝔞 c (R) is considered. [ABSTRACT FROM AUTHOR]