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

  1. left ideal
  2. right ideal

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*}

Date: nil

Author: Anton Zakrewski

Created: 2024-10-12 Sa 23:02