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Let $R$ be a commutative Noetherian ring, $\Phi$ a system of ideals of $R$and $M,X$ two $R$-modules. In this paper, we study the Artinianness andcofiniteness of the module $H^i_{\Phi}(M,X)$ which is an extension of thegeneralized local cohomology modules of Herzog.

Cofiniteness of generalized loca cohomology modules with respect to a system of ideals