Abstract
For a ring A, a ring extension B, and a fixed right A-module M, we give conditions under which a finitistic n-self-cotilting module M extends to a finitistic n-self-cotilting module K = Hom(A)(B, M) over the ring extension B. We prove that in case there is a ring homomorphism beta : B -> A (hence A and B are ring extensions of each other), K is M-reflexive and M similar to K (that is K vertical bar M in Mod-A and M vertical bar K in Mod-B), then M is finitistic n-self-cotilting module if and only if the induced module K = Hom(A)(B, M) is finitistic n-self-cotilting module.