Relation SEMIGROUP

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

Slots on this relation:

Instance-Of: Relation

Arity: 3

Equivalence Axioms:

(<=> (Semigroup ?Domain ?Op ?Id)
     (And (Binary-Operator-On ?Op ?Domain)
          (Associative ?Op ?Domain)
          (Identity-Element-For ?Id ?Op ?Domain)))

Other Related Axioms:

(<=> (Semigroup ?Domain ?Op ?Id)
     (And (Binary-Operator-On ?Op ?Domain)
          (Associative ?Op ?Domain)
          (Identity-Element-For ?Id ?Op ?Domain)))

(Subrelation-Of Abelian-Semigroup Semigroup)

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

(<=> (Ring ?Domain ?Plus-Op ?Zero-Id ?Mult-Op ?One-Id)
     (And (Abelian-Group ?Domain ?Plus-Op ?Zero-Id)
          (Semigroup ?Domain ?Mult-Op ?One-Id)
          (Distributes ?Mult-Op ?Plus-Op ?Domain)))