Exercise 4.2.2 (All of K is Algebraic over K)

Question

Show that every element of $K$ is algebraic over $K$.

Hassaan Naeem · Accepted Answer

\paragraph{Solution:}
Since $K$ is a field, $\forall k \in K: \exists -k \in K: k + (-k) = (-k) + k = 0$.
Therefore, $\forall k \in K$, we can choose $f(t) = t - k \in K[t]$. Hence we have that $f 
eq 0$
and $f(k) = k - k = 0$. Therefore $\forall k \in K, k$ is algebraic over $K$.

Exercise 4.2.2 (All of K is Algebraic over K)

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Exercise 4.2.2 (All of K is Algebraic over K)

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