Let R become the commutative ring. An '''R-algebra' occurs as ring S together by having a ring homomorphism from R to the center of S. Whenever S itself is commutative so these are known as the 'commutative R-algebra'.

A notion of R-algebra generalizes that of an associative algebra: if K occurs as field, then any associatory algebra above K occurs as K-algebra & vice-versa. Each R-algebra is too an R-module in an obvious manner.

Examples

Any ring S may be considered as an algebra across its center R. Any ring S may be considered as a Z-algebrthe inside a unique way. Every polynomial ring R[x₁, ..., xn] is a commutative R''-algebra.