Let $F/K$ be a normal finite extension where $F=F_1 \times F_2$ for subfields $F_1,F_2$ of $F$ where $F_1\ne F$ . Suppose $w$ is a normal basis element in $F/K$ for any $w\in F$ for which $Tr_{F/F_2}(w)$ is a normal basis element in $F_2/K$ . Then is it true that $K$ has prime characteristic ?
2026-02-22 19:55:09.1771790109
A statement about normal basis element , trace and characteristic of field
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