👉 In mathematics and abstract algebra, a semigroup is an associative and commutative monoid that has an identity element. A monoid is a set equipped with two binary operations satisfying certain properties that are common to all monoids. In a semigroup, every element has both an inverse and an identity.
A semigroup can be defined as a group in which the operation of multiplication (denoted by
) satisfies:
1. Commutativity: For any elements x and y, x
y
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