Definition:Ideal of Ring/Left Ideal

Definition
Let $\left({R, +, \circ}\right)$ be a ring, and let $\left({J, +}\right)$ be a subgroup of $\left({R, +}\right)$.

$J$ is a left ideal of $R$ iff:


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