\begin{definition}[Definition:Ideal of Ring/Left Ideal]
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {J, +}$ be a subgroup of $\struct {R, +}$.
$J$ is a '''left ideal of $R$''' {{iff}}:
:$\forall j \in J: \forall r \in R: r \circ j \in J$
that is, {{iff}}:
:$\forall r \in R: r \circ J \subseteq J$
\end{definition}