This is a good idea not showing the ribbon control for the users who will not be able to use it anymore.
The below script work if you want to hide the top navigation for the users who are least privileged or anonymous in SharePoint site and most of the options in ribbon are disabled for them.
1) Open your SharePoint master page
2) Locate this line:
3) Change it to:
4) Now find the end of the “s4-ribbonrow” tag and add following block right after it:
5) Save the new master page and publish it.