I get every 10 min many broadcast messages (maybe by other user). How can I disable those broadcast messages, in order to not see them on my screen?
If you mean something else, explain "broadcast messages" more precisely.
From your comments you seem to be still expecting an answer, so here is the one that you didn't read or didn't understand:
If someone has root on your machine, they can do anything they want to annoy you. Be glad they aren't killing your shells and removing your files. The only thing you can do to stop the annoyance is log out or ask the irritating person to stop. There is no technical solution; you are asking where the button is to make some kid stop throwing pebbles at you. There is no such button.
I am assuming that you are getting messages sent to your command-line/console window. If that is the case try this:
$ mesg n
If the messages don't stop they are likely coming from a user/process with root-level permissions, which cannot be stopped.
You mentioned a predictable 10 minute cycle. That could indicate the message is being generated by some daemon process. Maybe that process is using
syslog to record messages. If so, it is then possible that
syslog is configured to send messages that match certain criteria to users' terminals. Look through
/etc/syslog.conf for possible culprits. The documentation you can see by running
man syslog.conf should be able to get you started. I'd suggest starting with the "EXAMPLES" section.
loglevel=3 in your boot parameters.
The loglevel parameter suppresses all messages with a level greater than, or equal to, the number specified.
The levels are:
0 - Critical, system unusable 1 - Immediate action required 2 - Critical event 3 - Error 4 - Warning 5 - Notice 6 - Informative 7 - Debugging information