ideal
1. Definition
Let \(A\) be a ring and \(\mathfrak{a} \subseteq A\) an additive subgroup. Then \(\mathfrak{a}\) is said to be a two-sided ideal, if it is both a
i.e. for each \(\alpha \in A\) and \(a \in \mathfrak{a}\)
\begin{align*} \alpha \cdot a \in& \mathfrak{a} \\ a \cdot \alpha \in& \mathfrak{a} \end{align*}