List questions from field-theory

Published on 02 Mar 2019 - 22:59

25

Views

Meaning of a symbol regarding field.

Published on 27 Mar 2026 - 19:53

187

Views

Dimension of splitting field as the order of an element mod n

Published on 25 Mar 2026 - 22:30

157

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A proof of the Fundamental theorem of algebra without analysis, taking a different definition of $\mathbb C$?

Published on 03 Mar 2019 - 22:03

109

Views

Unramified extensions and base change

Published on 01 Apr 2026 - 16:59

149

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Verifying a $K$-basis for a primitive extension $K\subset K(\alpha)$

Published on 30 Mar 2026 - 18:09

403

Views

Counterexample to primitive element theorem

Published on 04 Mar 2019 - 14:40

64

Views

Let $L/Q$ be a field extension. Let $\sigma\in\textrm{Aut}_Q(L)$. Let $f(x) \in Q[x]$ be a polynomial. Show that $f(σ(α)) = σ(f(α))$ for all $α ∈ L.$

Published on 30 Mar 2026 - 18:10

85

Views

Is this element in the ring of integers?

Published on 04 Mar 2019 - 18:05

139

Views

automorphism group of splitting field of cubic polynomial over $\mathbb{Q}$

Published on 25 Mar 2026 - 20:15

82

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Derivative of Rational Function from Lang's Algebra

Published on 04 Mar 2019 - 23:20

182

Views

Field with one element and Chaitin's Constant

Published on 25 Mar 2026 - 7:42

94

Views

Probability of finding polynomials in a field

Published on 28 Mar 2026 - 11:12

135

Views

Showing linear independence of power basis of $\mathbb{Q}(\sqrt[4]{3})$ over $\mathbb{Q}$.

Published on 30 Mar 2026 - 18:06

1k

Views

Help proving polynomials division algorithm in $R[x]$ where $R$ is a domain.

Published on 25 Mar 2026 - 17:18

List Question

Equivalent definitions of perfect field

Meaning of a symbol regarding field.

Dimension of splitting field as the order of an element mod n

A proof of the Fundamental theorem of algebra without analysis, taking a different definition of $\mathbb C$?

Unramified extensions and base change

Verifying a $K$-basis for a primitive extension $K\subset K(\alpha)$

Counterexample to primitive element theorem

Let $L/Q$ be a field extension. Let $\sigma\in\textrm{Aut}_Q(L)$. Let $f(x) \in Q[x]$ be a polynomial. Show that $f(σ(α)) = σ(f(α))$ for all $α ∈ L.$

Is this element in the ring of integers?

automorphism group of splitting field of cubic polynomial over $\mathbb{Q}$

Derivative of Rational Function from Lang's Algebra

Field with one element and Chaitin's Constant

Probability of finding polynomials in a field

Showing linear independence of power basis of $\mathbb{Q}(\sqrt[4]{3})$ over $\mathbb{Q}$.

Help proving polynomials division algorithm in $R[x]$ where $R$ is a domain.

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