Distributivity Axiom

A Distributivity Axiom is an axiom that establishes a distributive operation relation between two operations.

• AKA: distributive law.
• Context:
  • It can typically facilitate algebraic manipulation with mathematical expressions.
  • It can often demonstrate the interaction of addition and multiplication in arithmetic.
  • It can range from being a basic distributivity axiom to being a generalized distributivity axiom, depending on its application.
  • It can integrate with linear algebra for vector operations.
• Examples:
  • algebraic structures, such as:
    • field for operations involving addition and multiplication.
  • Boolean algebra, which applies the distributive property to logical operations.
• Counter-Examples:
  • non-distributive operation, which lacks the distributive property.
• See: vector space, set axiom, field, Boolean algebra.

---