For $\unicode[STIX]{x1D6FC}$ an algebraic integer of any degree $n\geqslant 2$ , it is known that the discriminants of the orders $\mathbb{Z}[\unicode[STIX]{x1D6FC}^{k}]$ go to infinity as $k$ goes to infinity. We give a short proof of this result.

中文翻译：

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关于代数整数幂的判别式

对于 $ \ unicode [STIX] {x1D6FC} $一个任意 阶数$ n \ geqslant 2 $ 的代数整数，已知订单 $ \ mathbb {Z} [\ unicode [STIX] {x1D6FC} ^ { k}] $ 变为无穷大，而 $ k $ 变为无穷大。我们对此结果提供简短证明。