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Let $K$ be a field of positive characteristic $p$. Consider the system of $\mathbb F_p$-linear equations $$\left\{\begin{array}{ccl} a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n&=&b_1\\ a_{11}x^p_1+a_{...

Let $R = GF(q), q = p^r$, be a field with identity $e$, where $p$ is a prime number. Let $S=GF(q^n)$ be an extension of $R, n\geq 2$ and $K = GF(q^{mn})$ be an extension of $S$, where $m$ is prime. ...

Hellow. I'm sure that the following is truth, but I can't prove it. Let $R<S<K, R=\mathrm{GF}(q),\ S= \mathrm{GF}(q^n), \ K= \mathrm{GF}(q^{mn})$ be a chain of finite fields and $A = \{\theta\...