Patrick Morandi- Field and Galois Theory- Section 4- Exercise 11
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Let $k^p = k$, $K = k(x)$ and $F = k(u)$ for some $u \in K$. Show that $K/F$ is separable $\iff u \not\in K^p$.
79460
Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra.
68753
Elements in finite field extensions
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Atiyah-Macdonald, Exercise 5.4
153589
Integral basis of an extension of number fields
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
126127
A field extension of prime degree
65873
A proof for Atiyah-Macdonald Exercise I.21.iii
129420
Source to learn Galois Theory
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Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.
116628
Example of Galois extension whose Galois group is $A_4$
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
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Finite fields, existence of field of order $p^n$,proof help
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
69935
Field extensions of finite degree and primitive elements
144211
a second course in abstract algebra
125568
Construction of $p^n$ field