Let R be a commutative Noetherian ring and be an ideal of R. We intend to establish the dual of two Faltings’ Theorems for local homology modules of an Artinian module. As a consequence of this, we show that, if A is an Artinian module over a complete semi-local ring R and j is an integer such that  is Artinian for all  then the set  is finite.

Artinianness dimension, finiteness dimension, local cohomology modules, local homology modules, Matlis duality.