Actually idempotent comes from algebra, in particular from ring theory. An ideal is idempotent if its generator, say it a, multiplied by itself n times, equals the ring identity.
> Actually idempotent comes from algebra, in particular from ring theory. An ideal is idempotent if its generator, say it a, multiplied by itself n times, equals the ring identity.
The Wikipedia article you linked to defined it for ring elements rather than for ideals of rings and for n=2. I agree that it is sometimes useful to define it more generally where it is in respect to some integer n, analogous to nilpotence.
You may have encountered this notion first in ring theory which may have led to this impression, but it is by no means an idea originating from this specific context.
For example, another comment points out that in linear algebra, a projection operator is said to have the idempotence property.
See also https://en.wikipedia.org/wiki/Idempotent_(ring_theory)
The definition of idempotent used in IT, assumes that n=2.
Another concept stolen from Mathematics and misused in IT is Topology.