Let be an ideal of Noetherian local ring and a finitely generated -module of dimension . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to . Also we prove that for an arbitrary local ring (not necessarily complete), we have
Let be a local ring, an ideal of and a nonzero Artinian -module of Noetherian dimension with . We determine the annihilator of the top local homology module . In fact, we prove that
where denotes the smallest submodule of such that . As a consequence, it follows that for a complete local ring all associated primes of are minimal.
Let be an ideal of Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let , we will prove that for any integer
-
If
...
Download Results (CSV)