How can I remove this ribbon:
for specific users which has only read permissions?
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Use JS library SPServices from codeplex to get current user permissions: http://spservices.codeplex.com/wikipage?title=GetRolesAndPermissionsForCurrentUser
And then just hide the menu item with JS. The hardest part is to obtain the permissions, which can be done smoothly with SPServices.
You can add this JS to edited master page, or develop custom control, maybe just add web part to specific pages, where you want to hide the ribbon.
To avoid "flashing" of the ribbon maybe hide it first by CSS for everyone and then just display for the persons with specific permissions.