Linked from

The 12 pages that link to Semigroup, each with the reason it gives.

• Group theoryCompared with: Semigroups isolate associativity from the other group axioms.

• GroupCompared with: It retains associativity but drops the group’s identity and inverse requirements.

• Identity elementNarrower topic: Adding an identity to a semigroup produces a monoid.

• AssociativityBroader topic: Associativity is the defining law of a semigroup’s operation.

• Binary operationBroader topic: Associativity adds the defining extra law beyond a bare operation.

• Symmetry groupCompared with: Transformations that cannot be reversed may form a semigroup rather than a symmetry group.

• MonoidNarrower topic: A monoid is precisely a semigroup equipped with an identity element.

• Associative propertyBroader topic: Associativity alone, together with closure, defines the central law of a semigroup.

• Samuel EilenbergRelated: Finite semigroups encode the behavior of automata in Eilenberg’s algebraic theory.

• Algebraic structureCompared with: Associativity alone distinguishes semigroups from structures requiring identities or inverses.

• MagmaBroader topic: Adding associativity to a magma produces a semigroup.

• Algebra over a fieldCompared with: A semigroup has multiplication but lacks the linear structure and bilinearity of an algebra.