Like this from wikipedia on Monoid?<p>Suppose that S is a set and • is some binary operation S × S → S, then S with • is a monoid if it satisfies the following two axioms:<p>Associativity
   For all a, b and c in S, the equation (a • b) • c = a • (b • c) holds.
Identity element
    There exists an element e in S such that for every element a in S, the equations e • a = a • e = a hold.<p>In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique.[1] A monoid in which each element has an inverse is a group.