semigroup

In abstract algebra, a semigroup is an algebraic structure with a binary operation over its elements that is both closed and satisfies the associative property.  So for semigroup S with generic operator •:

for all a, b, c in S, the equation (a • b) • c = a • (b • c) holds.

Again, closure also holds for this operation. So:

•: S x S → S

A semigroup can be thought of as an associative magma.