Let R be a commutative Noetherian ring with nonzero identity, an ideal of R, M a finite R–module, X an arbitrary R–module, and n a non-negative integer. Here, we show that, in the Serre subcategories of the category of R–modules, how the generalized local cohomology modules, the ordinary local cohomology modules, and the extension modules behave similarly at the initial points i ≤ n. We conclude with some Artinianness and cofiniteness results for Hn M X , and some finiteness results for SuppR Hn M X and Ass R Hn M X .
