| 1. | This is not so obvious because xor is commutative and associative.
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| 2. | A field has, by definition, a commutative multiplication operation.
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| 3. | String concatenation is an associative, but non-commutative operation.
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| 4. | A complete ring has much simpler structure than a commutative ring.
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| 5. | The order is important because matrix multiplication is non-commutative.
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| 6. | He addressed the question of rigour by recourse to commutative algebra.
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| 7. | The partial differentiations of this function are commutative at that point.
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| 8. | This means that random variables form complex commutative *-algebras.
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| 9. | Indeed, the classical Boolean conjunction is both commutative and associative.
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| 10. | Many properties of commutative localization hold in this more general setting.
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