If a ring is commutative then it equals its center, so that a commutative R-algebra can be defined simply as a commutative ring A together with a commutative ring homomorphism .
If A ring is CoMmutaTivE TheN IT eQualS itS ceNter, So that A CommutaTivE R-aLgEbrA can be dEfInEd simplY AS A cOmMUTatIve ring a tOgetHer WitH a cOMmuTatIve rInG hoMOMorphism .