Can I define an abstract class for all derived Singletons in this way?

Question

This is my abstract class which must be derived each time I want to make a Singleton:

public abstract class Singleton<T> where T : Singleton<T>
{
    private static readonly Lazy<T> _instance = new Lazy<T>(() =>
    {
        var constructor = typeof(T).GetConstructor(BindingFlags.NonPublic |
            BindingFlags.Instance, null, new Type[0], null);

        return (T)constructor.Invoke(null);
    });
    public static T Instance { get { return _instance.Value; } }
    public Singleton() { }
}

So, every time I need to follow the Singleton design pattern, I can just make this:

sealed class Server : Singleton<Server>
{
    private Server() { }
    ...
}

Is this completely right, and, if not, why?

Edit:

• Added private constructor on derived class example and invoking on abstract base.

Edit:

• Reworked type parameter initialization.

Answer 1

No you can't because when you want to use new T() you should have a public constructor for it, and it's different from singleton definition. because in singleton you should have a private constructor, and in this case (public one) everyone can create new instance of your object and it's not a singleton.