Number Ring

A number ring is a mathematical structure consisting of a set of numbers equipped with two operations: addition and multiplication. These operations follow specific rules similar to regular numbers—addition and multiplication are associative, addition has an identity element (zero), multiplication has an identity (one), and multiplication distributes over addition. The set is closed under these operations, meaning applying them to elements in the set results in elements still within the set. Examples include the integers, rational numbers, and polynomial rings. Number rings help mathematicians understand properties of numbers, solutions to equations, and underlying algebraic structures.