A commutative monoid is a monoid whose operation is commutative. The natural numbers with addition form a commutative monoid that is not an abelian group, because positive elements have no additive inverses.

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A **monoid** is an algebraic structure that consists of a set equipped with a binary operation that satisfies two key properties: associativity and identity. More formally, a monoid is defined as a tuple \((M, \cdot, e)\), where: 1. **Set \(M\)**: This is a non-empty set of elements.