## Definition ## Given a [[commutative ring]] $R$, a __left $R$-algebra__ is a left $R$-[[module]] with a [[bilinear function]] $(-)\cdot(-): A \times A \to A$, and a __right $R$-algebra__ is a right $R$-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) * [[cancellation algebra]] * [[division algebra]]