# Definition:Ideal of Ring/Left Ideal

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## Definition

Let $\left({R, +, \circ}\right)$ be a ring.

Let $\left({J, +}\right)$ be a subgroup of $\left({R, +}\right)$.

$J$ is a left ideal of $R$ if and only if:

$\forall j \in J: \forall r \in R: r \circ j \in J$