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Artinianness of formal local cohomology modules

Shahram Rezaei — 2019

Commentationes Mathematicae Universitatis Carolinae

Let 𝔞 be an ideal of Noetherian local ring ( R , 𝔪 ) and M a finitely generated R -module of dimension d . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to 𝔪 . Also we prove that for an arbitrary local ring ( R , 𝔪 ) (not necessarily complete), we have Att R ( 𝔉 𝔞 d ( M ) ) = Min V ( Ann R 𝔉 𝔞 d ( M ) ) .

Annihilators of local homology modules

Shahram Rezaei — 2019

Czechoslovak Mathematical Journal

Let ( R , 𝔪 ) be a local ring, 𝔞 an ideal of R and M a nonzero Artinian R -module of Noetherian dimension n with hd ( 𝔞 , M ) = n . We determine the annihilator of the top local homology module H n 𝔞 ( M ) . In fact, we prove that Ann R ( H n 𝔞 ( M ) ) = Ann R ( N ( 𝔞 , M ) ) , where N ( 𝔞 , M ) denotes the smallest submodule of M such that hd ( 𝔞 , M / N ( 𝔞 , M ) ) < n . As a consequence, it follows that for a complete local ring ( R , 𝔪 ) all associated primes of H n 𝔞 ( M ) are minimal.

Finiteness of local homology modules

Shahram Rezaei — 2020

Archivum Mathematicum

Let I be an ideal of Noetherian ring R and M a finitely generated R -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 I M : = Ann R ( M / I M ) , we will prove that for any integer n If ...

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