List questions from field-theory

Published on 20 Mar 2026 - 10:34

575

Views

What is the algebraic closure of $K(x)$

Published on 17 Mar 2026 - 6:12

48

Views

When $k(a+b,c+d)\subseteq k(a,b,c,d)$ is Galois?

Published on 20 Mar 2026 - 15:35

606

Views

Minimal polynomial of $ab$, when those of $a$ and $b$ are known

Published on 25 Mar 2026 - 3:44

77

Views

Finding the minimal polynomial of $uv$, when those of $u$ and $v$ are given and of degree three

Published on 20 Mar 2026 - 23:11

75

Views

Extension of field, $\Bbb{R}(i \pi) = \Bbb{C} $

Published on 15 Mar 2026 - 3:32

172

Views

The roots after constructing an extension field by Kronecker's theorem

Published on 19 Mar 2026 - 17:40

263

Views

Embedding from Rational Numbers to Ordered Field is Order Preserving

Published on 20 Mar 2026 - 11:42

78

Views

Extension and restriction of involutions

Published on 22 Mar 2026 - 21:50

95

Views

A field extension of degree $\leq 2$

Published on 21 Mar 2026 - 13:11

821

Views

All maximal subfields of a Division Algebra are isomorphic.

Published on 22 Mar 2026 - 7:47

48

Views

Ideal $I_p$ in $\mathbb{F}_l[x]/(x^p -1)$ where $\frac{\epsilon p}{2} \leq \dim(I_p) < \epsilon p$

Published on 17 Mar 2026 - 20:39

84

Views

Fields generated by elements

Published on 19 Mar 2026 - 3:46

167

Views

Does every valuation ring arise out of a valuation?

Published on 25 Mar 2026 - 13:18

278

Views

Eigenvalues of an element in a field extension

Published on 19 Mar 2026 - 15:32

List Question

When a certain subfield of $\mathbb{C}(x,y^2)$ is Galois

What is the algebraic closure of $K(x)$

When $k(a+b,c+d)\subseteq k(a,b,c,d)$ is Galois?

Minimal polynomial of $ab$, when those of $a$ and $b$ are known

Finding the minimal polynomial of $uv$, when those of $u$ and $v$ are given and of degree three

Extension of field, $\Bbb{R}(i \pi) = \Bbb{C} $

The roots after constructing an extension field by Kronecker's theorem

Embedding from Rational Numbers to Ordered Field is Order Preserving

Extension and restriction of involutions

A field extension of degree $\leq 2$

All maximal subfields of a Division Algebra are isomorphic.

Ideal $I_p$ in $\mathbb{F}_l[x]/(x^p -1)$ where $\frac{\epsilon p}{2} \leq \dim(I_p) < \epsilon p$

Fields generated by elements

Does every valuation ring arise out of a valuation?

Eigenvalues of an element in a field extension

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