## Definition ## An **ideal** of a [[ring]] $R$ is an $R$-$R$-[[bimodule]] $I$ with a monic $R$-$R$-[[bimodule homomorphism]] $i:I \to R$. ## See also ## * [[commutative ring]] * [[bimodule]] * [[bimodule homomorphism]] * [[principal ideal]] * [[finitely generated ideal]] * [[prime ideal]] * [[irreducible ideal]]