commutative rings

A commutative ring is a mathematical structure that consists of a set of elements along with two operations: addition and multiplication. In this context, addition is similar to regular addition, while multiplication has the property that changing the order of the elements doesn’t affect the result (this is called commutativity). For example, in the ring of integers, both addition and multiplication are commutative. Commutative rings also include rules for combining elements (like distributing multiplication over addition) and have an additive identity (zero) and a multiplicative identity (one). They are foundational in many areas of mathematics, including algebra and number theory.