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monoid

 Definition/Summary A monoid is a set S with a binary operation S*S -> S that is associative and that has an identity element, thus making it a semigroup with an identity. A monoid where every element has an inverse is a group.

 Equations Associativity: $\forall a,b,c \in S ,\ (a \cdot b) \cdot c = a \cdot (b \cdot c)$ Identity e: $\forall a \in S,\ e \cdot a = a \cdot e = a$

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 Breakdown Mathematics > Algebra >> Group Theory