idempotent in a sentence

Examples

1. An idempotent matrix is always diagonalizable and its eigenvalues are either 0 or 1.
2. It can be shown that the only idempotent probability measures on a compact subgroups.
3. Likewise, the second axiom appears to be describing the commutation of two idempotents.
4. In an inverse semigroup the entire semilattice of idempotents is a p-system.
5. Kleene algebras are additively idempotent but not all quasi-regular semirings are so.
6. It is an example of a closure operator; all closure operators are idempotent functions.
7. Commutative idempotent quasigroups satisfying this additional property are called " Steiner quasigroups ".
8. Local rings also don't have such idempotents, but for a different reason.
9. As an illustration, a proof is given below for the idempotent law for union.
10. The elements in bold are the idempotents.