List questions from extension-field

Published on 25 Apr 2015 - 19:18

80

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Why do we have a basis?

Published on 26 Apr 2015 - 0:09

477

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Algebra vs field extension. Examples of finite dimensional algebras without primitive generators.

Published on 26 Apr 2015 - 18:03

370

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Why is F($\beta$) a subfield of F($\alpha$)?

Published on 27 Apr 2015 - 4:30

280

Views

Finite dimensional $\mathbb R$-algebras without zero divisors

Published on 27 Apr 2015 - 14:00

179

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Direct Proof of Divisibility in Extensions of Number Fields

Published on 11 Apr 2026 - 7:08

495

Views

Galois group of the field of all constructible complex numbers

Published on 11 Apr 2026 - 19:36

128

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Purely inseparable subextension of $F(x)$

Published on 29 Apr 2015 - 1:09

1.6k

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Using Zorn's lemma to show that every field has an algebraic closure.

Published on 29 Apr 2015 - 18:33

31

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Isomorphisms in characterisation of Galois extension

Published on 29 Apr 2015 - 19:13

62

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Automorphism of $\mathbb{Q}({\zeta_n})/\mathbb{Q}$

Published on 30 Apr 2015 - 3:37

307

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Existence of a unique subfield of degree dividing the degree of a given irreducible polynomial

Published on 30 Apr 2015 - 19:52

553

Views

Prove that the splitting field of $x^{p}-q$ for prime numbers $p,q$ is an extension of degree $p(p-1)$ in $\mathbb{Q}$.

Published on 27 Mar 2026 - 23:48

1k

Views

Irreducible polynomial over a field $k$ with $char\ k = p > 0$

Published on 27 Mar 2026 - 20:31

54

Views

Weakly normal polynomials and normal polynomials.

Published on 01 May 2015 - 20:53

List Question

$\mathbb Q [\sqrt{2} i]$ contains neither $\sqrt[4]{2}$ nor $\sqrt{2}$

Why do we have a basis?

Algebra vs field extension. Examples of finite dimensional algebras without primitive generators.

Why is F($\beta$) a subfield of F($\alpha$)?

Finite dimensional $\mathbb R$-algebras without zero divisors

Direct Proof of Divisibility in Extensions of Number Fields

Galois group of the field of all constructible complex numbers

Purely inseparable subextension of $F(x)$

Using Zorn's lemma to show that every field has an algebraic closure.

Isomorphisms in characterisation of Galois extension

Automorphism of $\mathbb{Q}({\zeta_n})/\mathbb{Q}$

Existence of a unique subfield of degree dividing the degree of a given irreducible polynomial

Prove that the splitting field of $x^{p}-q$ for prime numbers $p,q$ is an extension of degree $p(p-1)$ in $\mathbb{Q}$.

Irreducible polynomial over a field $k$ with $char\ k = p > 0$

Weakly normal polynomials and normal polynomials.

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