Semigroup Algebraic structure ⟨S, ∗⟩ Nonempty set SAssociativity axiom: ∀a,b,c ∈ S: a∗(b∗c)=(a∗b)∗c (Associative binary operation ∗)Closure Axiom: ∀a,b ∈ S: a∗b ∈ S (S is closed)