Managed Bean Inheritance

I want to create a superclass for several managed beans containing, among other things, an embedded managed @SessionScoped bean and @EJB. Next works

Super class:

@ManagedBean
@ViewScoped
public abstract class UserPageController implements Serializable {
    private static final long serialVersionUID = -6118448960678133445L;

    @ManagedProperty(value = "#{sessionController}")
    protected SessionController sessionController;

    private User user;
    private String userId;
    @EJB protected UserBean userBean;

    public UserPageController() {
    }

    public SessionController getSessionController() {
        return sessionController;
    }

    public void setSessionController(SessionController sessionController) {
        this.sessionController = sessionController;
    }

    //-------------------------------- User ------------------------------------
    public String getUserId() {
        return userId;
    }

    public void setUserId(String userId) {
        this.userId = userId;
    }

    public User getUser() {
        if (user == null) {
            if (getUserId() != null && sessionController.getLoggedInUser().getRole().isManager()) {
                User dbUser = userBean.findUser(Long.parseLong(userId));
                if (dbUser != null) {
                    setUser(dbUser);
                }
            } else {
                setUser(userBean.findUser(sessionController.getLoggedInUser().getId()));
            }
        }
        return user;
    }

    public void setUser(User user) {
        this.user = user;
    }

}

Using:

@ManagedBean
@ViewScoped
public class UserCompetenceController extends UserPageController implements Serializable {
    // Stuff that uses sessionController & userBean.
}

Is there a way to avoid annotating an abstract superclass as a managed bean? It seems somehow wrong, but without it, dependency injection will not work.