## Definition ## Given a [[ring]] $R$, a __$R$-algebra__ is a $R$-[[module]] with a [[bilinear function]] $(-)\cdot(-): A \times A \to A$. ## See also ## * [[module]] * [[Z-algebra]] * [[unital algebra]] * [[associative algebra]] * [[commutative algebra (module theory)]] * [[algebra (ring theory)]] (which are associative unital algebras) * [[commutative algebra (ring theory)]] (which are commutative associative unital algebras)