Received February 6, 2018. Published online June 4, 2019.
Abstract: Let $\mathcal I$ be a set of ideals of a commutative Noetherian ring $R$. We use the notion of $\mathcal I$-closure operation which is a semiprime closure operation on submodules of modules to introduce the class of $\mathcal I$-Laskerian modules. This enables us to investigate the set of associated prime ideals of certain $\mathcal I$-closed submodules of local cohomology modules.
Keywords: associated prime ideals; Grothendieck spectral sequence; local cohomology module; semiprime closure operation