| 21. | There is a structure theorem for commutative semigroups in terms of semilattices.
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| 22. | Infinitary generalizations of commutative semigroups have sometimes been considered by various authors.
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| 23. | This makes " S " an idempotent, commutative quasigroup.
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| 24. | If is commutative of if is contained in the algebra.
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| 25. | A similar proof shows that every Boolean ring is commutative:
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| 26. | The discriminant can even be defined for polynomials over any commutative ring.
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| 27. | For this reason, ring addition is commutative in general.
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| 28. | The knot sum of oriented knots is commutative and associative.
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| 29. | These germs can be added and multiplied and form a commutative ring.
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| 30. | The associative property is closely related to the commutative property.
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