Let $\mathbb Z[i]=\{a+bi \mid a,b∈ℤ\}$ be a subring of $ℂ$. Consider two principal ideals $I=(7)$ and $J=(13)$ in $\mathbb Z[i]$. Is the ideal $I$ maximal? Is the ideal $J$ maximal?
2026-04-04 13:40:42.1775310042
Maximal ideals in $\mathbb Z[i]$
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HINT for second question: $$ 13 = (3 + 2i)(3 - 2i) $$