| 11. | Furthermore, disjunction is not idempotent and does not distribute over conjunction.
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| 12. | The merge function is commutative, associative, and idempotent.
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| 13. | The only idempotent contained in the Jacobson radical of a ring is 0.
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| 14. | Idempotent matrices arise frequently in regression analysis and econometrics.
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| 15. | The idempotent and zero-divisor conjectures have implications for geometric group theory.
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| 16. | There is a close relationship between the subgroups of a semigroup and its idempotents.
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| 17. | Each subgroup contains exactly one idempotent, namely the identity element of the subgroup.
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| 18. | That is, each factor has two idempotents.
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| 19. | This shows that integral domains and division rings don't have such idempotents.
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| 20. | A bounded semilattice is an idempotent commutative monoid.
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