# Category:Associativity

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This category contains results about **Associativity**.

Definitions specific to this category can be found in Definitions/Associativity.

Let $S$ be a set.

Let $\circ : S \times S \to S$ be a binary operation.

Then $\circ$ is **associative** if and only if:

- $\forall x, y, z \in S: \paren {x \circ y} \circ z = x \circ \paren {y \circ z}$

## Subcategories

This category has the following 7 subcategories, out of 7 total.

### E

### G

### S

## Pages in category "Associativity"

The following 22 pages are in this category, out of 22 total.

### A

### C

### O

- Operation Induced by Permutation on Semigroup is not necessarily Associative
- Operation over which Every Commutative Associative Operation is Distributive is either Left or Right Operation
- Operation which is Left Distributive over Every Commutative Associative Operation is Right Operation
- Operation which is Right Distributive over Every Commutative Associative Operation is Left Operation