Question
Let $S=\{a+b i \mid a, b \in Z, b$ is even $\}$. Show that $S$ is a subring of $Z[i]$, but not an ideal of $Z[i]$.
Step 1
To do this, we need to show that $S$ is closed under addition and multiplication, and that it contains the additive identity and the additive inverse of each of its elements. Show more…
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