List questions from extension-field

Published on 14 Aug 2015 - 8:40

199

Views

Question about the splitting field of a finite separable extension

Published on 12 Apr 2026 - 2:54

750

Views

Unique extension of the absolute value

Published on 11 Apr 2026 - 13:51

1.1k

Views

Quadratic field extensions and complex conjugation

Published on 12 Apr 2026 - 0:48

72

Views

Degree of a splitting field of a polynomial

Published on 11 Apr 2026 - 16:45

275

Views

A Field Extension of a Cyclic Galois Group is Galois

Published on 11 Apr 2026 - 22:16

3.2k

Views

What's so special about quadratic extensions?

Published on 11 Apr 2026 - 16:49

207

Views

Existence of an intermediate field $K\subseteq M \subseteq L$ such that $[L:M]=p$

Published on 23 Aug 2015 - 11:25

350

Views

field extension $F\subset E$ with both separable and inseparable elements

Published on 29 Aug 2015 - 15:07

202

Views

Understanding the connection of the roots of an irreducible polynomial and a basis for field extensions

Published on 01 Sep 2015 - 17:43

584

Views

Prove: $B=\{x\in \Bbb R\mid x^2\in\Bbb Q\}$ is countable

Published on 03 Apr 2026 - 18:10

1.7k

Views

Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.

Published on 09 Sep 2015 - 2:12

623

Views

A question on the construction of the complex numbers and field extensions

Published on 11 Apr 2026 - 17:30

102

Views

First class example and i have no clue what to do

Published on 15 Sep 2015 - 1:50

592

Views

Question regarding the proof of the Fundamental Theorem of Algebra

Published on 08 Apr 2026 - 6:36

List Question

If $E/F$ is finite divisible, then it is separable.

Question about the splitting field of a finite separable extension

Unique extension of the absolute value

Quadratic field extensions and complex conjugation

Degree of a splitting field of a polynomial

A Field Extension of a Cyclic Galois Group is Galois

What's so special about quadratic extensions?

Existence of an intermediate field $K\subseteq M \subseteq L$ such that $[L:M]=p$

field extension $F\subset E$ with both separable and inseparable elements

Understanding the connection of the roots of an irreducible polynomial and a basis for field extensions

Prove: $B=\{x\in \Bbb R\mid x^2\in\Bbb Q\}$ is countable

Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.

A question on the construction of the complex numbers and field extensions

First class example and i have no clue what to do

Question regarding the proof of the Fundamental Theorem of Algebra

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