## Definition ## Given a [[commutative ring]] $R$, an __commutative $R$-algebra__ is a commutative ring $A$ with a [[commutative ring homomorphism]] $f:R \to A$ ## Properties ## An commutative algebra in ring theory is an [[commutative associative algebra (module theory)|commutative]] [[associative algebra|associative]] [[unital algebra|unital]] [[algebra (module theory)|algebra]] in [[module]] theory. ## See also ## * [[commutative ring]] * [[polynomial ring]] * [[algebra (ring theory)]] * [[algebra (module theory)]]