After I was rescued from the Linux Mint Mate user, I have now migrated to Ubuntu Mate, but miss the language flag in the greeter. In Mint I could with a new application with the switch flag to change the system language.
Translated by Google Translate
Nachdem ich Jahre lang LInux-Mint-Mate-user war, bin ich nun au Ubunt-Mate umgestiegen, vermisse aber die Sprachflagge im Anmeldefenter. Bei Mint konnte ich mit einer Neuanmeldung mit wechseln der Falgge die Systemsprache wechseln.
I'm not sure the English translation here. But I know you can change the language, easy in, say, LibreOffice go through the Tools menu
Translated by Google Translate
Ich bin nicht sicher, der deutschen Übersetzung hier . Aber ich weiß, Sie die Sprache ändern können, leicht in , sagen wir, Libreoffice durch zum Menü Extras gehen
Hi there. I attempted to translate the posts, since the forum still operates in English only, this could change.
In lightdm-gtk-greeter, the language locale appears in the top-right, like this:

Languages can be added or removed from System → Preferences → Personal → Language Support:

When languages are installed to the system, they must be applied system wide:

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Than k you for the answer. But all this I had already made . In the off - and on-window for the userchanging nevertheless can not , like mint , change the language. The only way, that I find out, is the drag of the sekond language on the first place and then to do the userchange
Hi @Wolfdietrich_Wohinz,
the language tool in Ubuntu 16.04 is defective at the moment so please wait a short while until it is updated and fixed!.
I use German and English on a daily basis myself and I have problems with the tool myself, in the meantime; you can take a look at the language guide but as far as I am aware, there is no flag setting for Ubuntu or Ubuntu Mate!, take a look in Dconf Editor for a setting that states “Show flags” or something like that but I cannot find it !. 
How to change the language settings in Ubuntu
Zur Zeit ist die Sprach Tool defekt, Bitte Geduld haben bis einen Fix Vorhanden ist!. 