noun
definition
An idempotent element.
definition
An idempotent structure.
adjective
definition
Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.
definition
Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.
example
Every group has a unique idempotent element: namely, its identity element.
definition
Said of a binary operation: that all of the distinct elements it can operate on are idempotent (in the sense given just above).
example
Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself.
definition
Said of an algebraic structure: having an idempotent operation (in the sense above).