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Weakly Laskerian modules and weak cofiniteness
Miskolc Mathematical Notes
Let R be a commutative Noetherian ring, a an ideal of R. It is shown that if a D .x 1 ; : : : ; x t /, and M is an R-module, then Ext i R .R=a; M / is weakly Laskerian for all i iff Tor R i .R=a; M / is weakly Laskerian for all i iff the Koszul cohomology module H i .x 1 ; : : : ; x t I M / is weakly Laskerian for all i. Furthermore, each of these coditions imply that M=a n M is weakly Laskerian for all n 2 N. In Section 3, we show that if M is an R-module with Supp M Â V .a/, then M isdoi:10.18514/mmn.2014.608 fatcat:pulon5ubjbcdlovf3ikkfbamiy