I copied your command, because I had the same entries. Here are the results:
materalph@materalph-System-Product-Name:~$ sudo dpkg --remove mate-screensaver mate-screensaver-common
[sudo] password for materalph:
dpkg: dependency problems prevent removal of mate-screensaver:
mate-gnome-main-menu-applet depends on mate-screensaver.
ubuntu-mate-desktop depends on mate-screensaver.
ubuntu-mate-core depends on mate-screensaver.
dpkg: error processing package mate-screensaver (--remove):
dependency problems - not removing
dpkg: dependency problems prevent removal of mate-screensaver-common:
mate-screensaver depends on mate-screensaver-common (= 1.12.0-1).
dpkg: error processing package mate-screensaver-common (--remove):
dependency problems - not removing
Errors were encountered while processing:
mate-screensavermateralph@materalph-System-Product-Name:~$ sudo dpkg --remove mate-screensaver mate-screensaver-common
[sudo] password for materalph:
dpkg: dependency problems prevent removal of mate-screensaver:
mate-gnome-main-menu-applet depends on mate-screensaver.
ubuntu-mate-desktop depends on mate-screensaver.
ubuntu-mate-core depends on mate-screensaver.
dpkg: error processing package mate-screensaver (--remove):
dependency problems - not removing
dpkg: dependency problems prevent removal of mate-screensaver-common:
mate-screensaver depends on mate-screensaver-common (= 1.12.0-1).
dpkg: error processing package mate-screensaver-common (--remove):
dependency problems - not removing
Errors were encountered while processing:
mate-screensaver
mate-screensaver-common
materalph@materalph-System-Product-Name:~$
mate-screensaver-common
materalph@materalph-System-Product-Name:~$
Thanks
mt