List questions from field-theory

Published on 14 Apr 2026 - 7:58

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Let $a$ and $b$ belong to some extension of $F$ and let $b$ be algebraic over $F$. Prove that $[F(a, b):F(a)] \leq [F(a, b):F]$.

Published on 17 Apr 2026 - 6:59

489

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Find the minimal polynomial of $a^i \in F_{16}$, for all $1 \leq i \leq 14$

Published on 15 Apr 2026 - 19:57

594

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Isomorphism Field of Fractions

Published on 09 Apr 2026 - 13:15

176

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$F_p(a)$ contains all the roots of $f$

Published on 17 Apr 2026 - 4:38

426

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Intermediate Radical Extension Paradox

Published on 10 Apr 2026 - 2:17

2.8k

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Show that the Galois group is cyclic

Published on 11 Apr 2026 - 17:59

1.7k

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If $x^p - a$ is reducible in a characteristic $p$ field, then it has a root.

Published on 16 Apr 2026 - 5:31

348

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Metaphor/Analogies for Rings and Fields?

Published on 13 Apr 2026 - 18:43

39

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Understanding this Abstract Algebra Theorem

Published on 10 Apr 2026 - 13:57

46

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what argument can we prove this fact??

Published on 14 Apr 2026 - 12:20

1.5k

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The simplest radical extension with a non-radical subextension

Published on 15 Apr 2026 - 7:56

74

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order of $Z[i]/\langle 2+4i\rangle$

Published on 15 Apr 2026 - 8:15

543

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How to approach construction of ring homomorphisms?

Published on 09 Apr 2026 - 20:06

1.3k

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Prime ideals in $F[x]$ when $F$ is a field

Published on 17 Apr 2026 - 8:59

List Question

finding galois extension isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_4$ and $Q_8$

Let $a$ and $b$ belong to some extension of $F$ and let $b$ be algebraic over $F$. Prove that $[F(a, b):F(a)] \leq [F(a, b):F]$.

Find the minimal polynomial of $a^i \in F_{16}$, for all $1 \leq i \leq 14$

Isomorphism Field of Fractions

$F_p(a)$ contains all the roots of $f$

Intermediate Radical Extension Paradox

Show that the Galois group is cyclic

If $x^p - a$ is reducible in a characteristic $p$ field, then it has a root.

Metaphor/Analogies for Rings and Fields?

Understanding this Abstract Algebra Theorem

what argument can we prove this fact??

The simplest radical extension with a non-radical subextension

order of $Z[i]/\langle 2+4i\rangle$

How to approach construction of ring homomorphisms?

Prime ideals in $F[x]$ when $F$ is a field

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