Let A be a finite-dimensional k-algebra,where k is a fixed field. All modules of A are finitely generated left modules. Suppose X is an A-module. We denote by add(X) the full subcategory of A-modules consisting of all direct summands of direct sum of finitely many copies of X. $D$ is the usual k-duality $Hom_k(-,k)$, $\nu _A$ is the Nakayama functor $DHom_A(-,_{A}A)$
Recall that the module X is called a generator over A if $add(_{A}A) \subseteq add(X)$, a cogenerator if $add(D(A_A)) \subseteq add(X)$, and a generator-cogenerator if it is both a generator and a cogenerator over A.
Can anyone tell me how to get the following results:
1):Let V be a generator over A with $B := End_A(V)$.Then $Hom_A(V,I)$ is an injective B-module for every injective A-module I.
2): If V is a generator-cogenerator, then each projective-injective B-module is precisely of the form $Hom_A(V,I)$ with I an injective A-module.
Also I want to know is there any other results of the modules of $B=End_A(V)$ for a A-module V?