Prime Splitting and Common $N$-Index Divisors in Radical Extensions: Part $p=2$

This article title suggests a highly specialized mathematical research paper. The focus is on prime splitting, a concept in number theory, within the context of radical extensions of fields. The inclusion of "Part p=2" indicates this is likely a segment of a larger work, possibly focusing on the case where the prime number p equals 2. The title is technical and aimed at a specific audience familiar with abstract algebra and number theory.