Ideal of Ring/Examples
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Examples of Ideals of Rings
Set of Even Integers
The set $2 \Z$ of even integers forms an ideal of the ring of integers.
Order 2 Matrices with some Zero Entries
Let $R$ be the set of all order $2$ square matrices of the form $\begin{pmatrix} x & y \\ 0 & z \end{pmatrix}$ with $x, y, z \in \R$.
Let $S$ be the set of all order $2$ square matrices of the form $\begin{pmatrix} x & y \\ 0 & 0 \end{pmatrix}$ with $x, y \in \R$.