On the Local Cohomology Modules Defined by a Pair of Ideals and Serre Subcategory

Khadijeh Ahmadi-Amoli, Mir Yousef Sadeghi


This paper is concerned with the relation between local
cohomology modules defined by a pair of ideals and Serre classes of
R-modules. Let R be a commutative Noetherian ring, I , J be two
ideals of R and M be an R-module. Let a 2 ˜W (I, J) and t 2 N0
be such that Extt
R(R/a,M) 2 S and Extj
I,J (M)) 2 S for all
i < t and all j > 0. Then for any submodule N of Ht
I,J (M) such that
R(R/a,N) 2 S, we obtain HomR(R/a,Ht
I,J (M)/N) 2 S.


Local cohomology modules defined by a pair of ideals, local cohomology, goldie dimension, (I, J)-minimax modules, serre subcategory, (S, I, J)-cominimax modules, associated primes

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