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Q48Section II (Mathematics)48 of 190

Z[−p]\mathbb{Z}[\sqrt{-p}] fails unique factorization for every odd prime pp

Let pp be an odd prime number and Z[−p]={a+b−p∣a,b∈Z}(⊆C)\mathbb{Z}[\sqrt{-p}]=\{a+b\sqrt{-p}\mid a,b\in\mathbb{Z}\} (\subseteq\mathbf C). Then the ring Z[−p]\mathbb{Z}[\sqrt{-p}] is:

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