Common
Semigroup
Algebraic structure
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. In mathematical analysis, the term also appears in the theory of one-parameter operator semigroups: see C0-semigroup. The binary operation of a semigroup is most often denoted multiplicatively: x ⋅ y {\displaystyle x\cdot y} , or simply x y {\displaystyle xy} , denotes the result of applying the semigroup operation to the ordered pair ( x , y ) {\displaystyle (x,y)} . Associativity is formally expressed as that ( x ⋅ y ) ⋅ z = x ⋅ ( y ⋅ z ) {\displaystyle (x\cdot y)\cdot z=x\cdot (y\cdot z)} for all...
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