Let $A$ be a finite dimensional algebra over a field K. $E$ is an injective $A$ module. $\nu=DHom_A(-,A)$ is the Nakayama functor. $add(E)$ is the full subcategory of $A$-module consisting of all direct summands of direct sum of finitely many copies of $E$.
How to get that $add(E)=add(\nu(E))$ equivalent to $add(soc(E))\cong add(top(E))$?
