Commutative Ring

A commutative ring is a mathematical system where you can add and multiply elements, similar to regular numbers, with some specific rules. In such a ring, the order of multiplication doesn't matter (commutative property), meaning \(a \times b = b \times a\). It also allows for addition and multiplication to follow familiar rules like associativity and distributivity. Examples include integers, polynomials, and matrices under certain conditions. Commutative rings are fundamental structures in algebra, helping mathematicians understand and work with various mathematical objects that share these fundamental properties.