List questions from field-theory

Published on 29 Mar 2026 - 3:52

480

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Is a finitely generated torsion-free R-module free over R if R is an integral domain?

Published on 25 Mar 2026 - 11:54

123

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Is there a ring whose total ring of fractions is not a field?

Published on 17 May 2019 - 2:23

108

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Is every point in the spectrum of a ring $R$ closed?

Published on 25 Mar 2026 - 12:26

135

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Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Published on 26 Mar 2026 - 14:34

41

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Cardinalities of Galois extensions and compositum

Published on 01 Apr 2026 - 13:09

51

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$A$ algebraic over $B$, $B$ algebraic over $C$. $A$ algebraic over $C$?

Published on 17 May 2019 - 19:32

87

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Field extension of degree $p^n$

Published on 01 Apr 2026 - 13:09

101

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Irreducibility of $t ^ { 4 } + t - 1$ over $\mathbb{F}_{25}$

Published on 29 Mar 2026 - 3:53

37

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Two questions on the ring S := {a+bs : a,b ∈ R}

Published on 18 May 2019 - 17:26

136

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How to prove $(-1)\cdot x = -x$ in a field?

Published on 19 May 2019 - 8:39

151

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Showing that $\sqrt{5} \in \mathbb{Q}(\sqrt[p]{2} + \sqrt{5})$

Published on 31 Mar 2026 - 20:26

360

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Is the ideal $I=(X+Y,X-Y)$ in the polynomial ring $\mathbb{C}[X,Y]$ a prime ideal?

Published on 29 Mar 2026 - 13:47

38

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$f(x)=(x-a)(x-a_2)...(x-a_n)\in F[x]$ where $F$ is a field and $a_j\in $ for $j=1,2,...,n$ has no repeated roots iff gcd$(f(x),f'(x))=1\in F[x]$

Published on 29 Mar 2026 - 14:25

50

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Zeros in Splitting Factor Rings

Published on 25 Mar 2026 - 12:22

List Question

Must Additive Inverse elements be opposite in sign?

Is a finitely generated torsion-free R-module free over R if R is an integral domain?

Is there a ring whose total ring of fractions is not a field?

Is every point in the spectrum of a ring $R$ closed?

Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Cardinalities of Galois extensions and compositum

$A$ algebraic over $B$, $B$ algebraic over $C$. $A$ algebraic over $C$?

Field extension of degree $p^n$

Irreducibility of $t ^ { 4 } + t - 1$ over $\mathbb{F}_{25}$

Two questions on the ring S := {a+bs : a,b ∈ R}

How to prove $(-1)\cdot x = -x$ in a field?

Showing that $\sqrt{5} \in \mathbb{Q}(\sqrt[p]{2} + \sqrt{5})$

Is the ideal $I=(X+Y,X-Y)$ in the polynomial ring $\mathbb{C}[X,Y]$ a prime ideal?

$f(x)=(x-a)(x-a_2)...(x-a_n)\in F[x]$ where $F$ is a field and $a_j\in $ for $j=1,2,...,n$ has no repeated roots iff gcd$(f(x),f'(x))=1\in F[x]$

Zeros in Splitting Factor Rings

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