Abstract
Let R be a commutative Noetherian ring, a an ideal of R, M an R-module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of AF modules. The main result is that if the R-module Ext t R (R/a,M) is finite (finitely generated), H i a (M) is a-cofinite for all i < t and H t a (M) is minimax then H t a (M) is a-cofinite. As a consequence we show that if M and N are finite R-modules and H i a (N) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology module H t a (M,N) is finite.
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Laleh, S.S., Sadeghi, M.Y. & Mostaghim, M.H. Some results on the cofiniteness of local cohomology modules. Czech Math J 62, 105–110 (2012). https://doi.org/10.1007/s10587-012-0019-4
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DOI: https://doi.org/10.1007/s10587-012-0019-4