The word
simple has a
mathematical meaning.
Def A group is said to be simple if it has no normal subgroups other than itself and the trivial subgroup.
Def A ring is said to be simple if it has no two-sided ideals
other than itself and {0}.
It is used for other algebraic structures too, with an analagous meaning, whenever there is a concept of an ideal.
The Alternating group An, for n>=5,
is an example of a simple group. The Weyl algebra is an
example of a simple ring.