High Quality Content by WIKIPEDIA articles! In mathematics, a semigroup is an algebraic structure consisting of a nonempty set S together with an associative binary operation. In other words, a semigroup is an associative magma. The terminology is derived from the anterior notion of a group. A semigroup differs from a group in that for each of its elements there may not exist an inverse; further, there may not exist an identity element. The binary operation of a semigroup is most often denoted multiplicatively: x * y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y).

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