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