Alternativity

In mathematics alternativeness is a weakening of the associative law.

Definition

· A link is called alternative if the two statements below for all and apply:

And

Importance

Is a shortcut associative, you can omit the parentheses in three - and multi-unit expressions:

Does not apply the associative law, all brackets must remain standing. Does the alternativeness, the brackets can leave you at least when or if. In particular, the same factors to powers which can be summarized. This means that it is possible to summarize the nature of products.

Each associative link is automatically alternatively.

Examples

• Alternatively, a body, a generalized body is required by the multiplication in place of the associative law only alternativeness. In contrast to a body, the multiplication needs to be not commutative.

• The real octonions form such an alternative body. Your multiplication is an alternative, but neither associative nor commutative.