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according to the study unit, the commutative property means

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1.Commutative ring

algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra

2.Algebra over a field

as algebraic geometry, unital associative commutative algebra. Replacing the field of scalars by a commutative ring leads to the more general notion of

3.Associative algebra

a commutative ring. In this article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative

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