Semigroup

A semigroup is a mathematical concept consisting of a set of elements combined with an operation (like addition or multiplication) that satisfies the property of associativity. This means that when applying the operation to three elements, the grouping doesn't matter: (a * b) * c = a * (b * c). Unlike groups, semigroups do not necessarily have identity elements or inverses. They are fundamental in structures where combining elements consistently is essential, such as in computer science, algebra, and formal language theory, providing a framework for understanding how operations on sets behave when grouped in different ways.