A commutative ring is a mathematical structure consisting of a set equipped with two operations: addition and multiplication. In a commutative ring, addition is associative and commutative, meaning the order of the elements does not affect the result. Additionally, multiplication is also associative and commutative, and the distributive property holds, linking the two operations. In a commutative ring, there is an additive identity (usually denoted as 0) and a multiplicative identity (usually denoted as 1). Some elements may have inverses, leading to the concept of a field if every non-zero element has a multiplicative inverse. Examples of commutative rings include the set of integers, denoted as ℤ, and polynomial rings.