Relation COMMUTATIVE

• Defined in theory: Abstract-algebra
• Source code: abstract-algebra.lisp

Slots on this relation:

Instance-Of: Relation

Arity: 2

Equivalence Axioms:

(<=> (Commutative ?Op ?Domain)
     (Forall (?X ?Y)
             (=> (Instance-Of ?X ?Domain)
                 (Instance-Of ?Y ?Domain)
                 (= (Value ?Op ?X ?Y) (Value ?Op ?Y ?X)))))

Other Related Axioms:

(<=> (Commutative ?Op ?Domain)
     (Forall (?X ?Y)
             (=> (Instance-Of ?X ?Domain)
                 (Instance-Of ?Y ?Domain)
                 (= (Value ?Op ?X ?Y) (Value ?Op ?Y ?X)))))

(<=> (Abelian-Semigroup ?Domain ?Op ?Id)
     (And (Semigroup ?Domain ?Op ?Id) (Commutative ?Op ?Domain)))

(<=> (Abelian-Group ?Domain ?Op ?Id)
     (And (Group ?Domain ?Op ?Id) (Commutative ?Op ?Domain)))

(<=> (Field ?Domain ?Plus-Op ?Zero-Id ?Mult-Op ?One-Id)
     (And (Division-Ring ?Domain ?Plus-Op ?Zero-Id ?Mult-Op ?One-Id)
          (Commutative ?Plus-Op ?Domain)))