Let R be a commutative Noetherian ring and a 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 Hi (A) a is Artinian for all i < j, then the set CoassR(H j (A)) a is finite.
