Commutative Ring If multiplication is commutative , that is For all a and b in R , the equation a â cents b = b â cents a holds , then the ring is called a commutative ring . Although ring addition is commutative , so that for every a , b in R , a + b = b + a , ring multiplication is not required to be commutative ; a Â b need not equal b Â a for all a , b in R. Rings that also satisfy commutativity for multiplication are called commutative rings .