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Let be a set of ideals of a commutative Noetherian ring . We use the notion of -closure operation which is a semiprime closure operation on submodules of modules to introduce the class of -Laskerian modules. This enables us to investigate the set of associated prime ideals of certain -closed submodules of local cohomology modules.
Let be a commutative Noetherian ring with identity and an ideal of . It is shown that, if is a non-zero minimax -module such that for all , then the -module is -cominimax for all . In fact, is -cofinite for all . Also, we prove that for a weakly Laskerian -module , if is local and is a non-negative integer such that for all , then and are weakly Laskerian for all and all . As a consequence, the set of associated primes of is finite for all , whenever and...
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