Suppose that (R, +,×) and (R′, ⊕, ⊗) are rings. An isomorphism between them is a one‐to‐one onto mapping f from the set R to the set R′ such that, for all a and b in R,

If there is an isomorphism between two rings, the rings are isomorphic to each other and, as with isomorphic groups, the two have essentially the same structure.