Definition:Ideal of Ring/Left Ideal

Definition
Let $\struct {R, +, \circ}$ be a ring.

Let $\struct {J, +}$ be a subgroup of $\struct {R, +}$.

$J$ is a left ideal of $R$ :
 * $\forall j \in J: \forall r \in R: r \circ j \in J$

that is, :
 * $\forall r \in R: r \circ J \subseteq J$

Also see

 * Definition:Right Ideal of Ring