Editing Group action (section)

=== Linear actions ===
{{Main|Group representation}}
If {{math|''g''}} acts by [[Linear map|linear transformations]] on a [[Module (mathematics)|module]] over a [[commutative ring]], the action is said to be [[Irreducible representation|irreducible]] if there are no proper nonzero {{math|''g''}}-invariant submodules. It is said to be ''[[Semi-simplicity|semisimple]]'' if it decomposes as a [[direct sum]] of irreducible actions.