This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the existence of such elements. We then derive concrete existence results for a special class of intermediate extensions.

中文翻译：

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具有规定迹线的有限域生成器

本文探讨了有限域扩展中原始元素的存在和分布，在几个中间域扩展中具有规定的迹线。我们的主要结果提供了一个类似不等式的条件来确保这些元素的存在。然后我们为一类特殊的中间扩展推导出具体的存在结果。