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What does commutative mean?

Looking for the meaning or definition of the word commutative? Here's what it means.

Adjective
  1. (algebraic structure) Having a commutative operation.
  2. (mathematics) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
  3. (mathematics) Such that the order in which the operands are taken does not affect their image under the operation.
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What are the associative, commutative, distributive, and equality properties?
The second difficulty was more damaging and, to a degree, commutative with the first.
An operation is commutative if you can change the order of the numbers involved without changing the result.
Of course, the relationship between painting and philosophy is not entirely commutative.
Using the fact that polynomial rings are Noetherian, show that every finitely generable commutative ring is finitely presentable.
So, the addition and multiplication we are used to using are commutative.

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