21. An idempotent matrix is always diagonalizable and its eigenvalues are either 0 or 1. 22. It can be shown that the only idempotent probability measures on a compact subgroups. 23. Likewise, the second axiom appears to be describing the commutation of two idempotents . 24. In an inverse semigroup the entire semilattice of idempotents is a p-system. 25. Kleene algebras are additively idempotent but not all quasi-regular semirings are so. 26. It is an example of a closure operator; all closure operators are idempotent functions. 27. Commutative idempotent quasigroups satisfying this additional property are called " Steiner quasigroups ". 28. Local rings also don't have such idempotents , but for a different reason. 29. As an illustration, a proof is given below for the idempotent law for union. 30. The elements in bold are the idempotents .
