Warum wird der Button nicht hinzugefügt?

import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import javax.swing.JButton;
import javax.swing.JFrame;

public class frame extends JFrame implements ActionListener{

    private JButton exit;

    public static void main(String[] args) {
        JFrame frame = new JFrame();
        frame.setBounds(0, 0, 500, 500);
        frame.setVisible(true);
        frame.setLayout(null);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

    }


    public frame(String title){

        super (title);
        JButton exit;
        exit = new JButton("Schließen");
        exit.setBounds(375,400,100,50);
        exit.addActionListener(this);
        add (exit);
    }




    @Override
    public void actionPerformed(ActionEvent e) {
        if(e.getSource() == exit){
            System.exit(0);
        }
    }

}