List questions from abstract-algebra

Published on 11 Apr 2026 - 16:11

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Divisibility conditions

Published on 14 May 2026 - 0:20

255

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What is Gal$_\mathbb{Q}(x^4 + 5x^3 + 10x + 5)$?

Published on 10 May 2026 - 16:39

626

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Pontryagin duality of finite groups

Published on 10 May 2026 - 12:53

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Finite field of with multiplication group isomorphic to the cyclic group of order $17$

Published on 15 Apr 2026 - 7:46

634

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$f (e_G )=e_H $ is necessary for Monoid homomorphisms

Published on 13 May 2026 - 1:59

44

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If $\hat{O}$ is compact, then $\frac{\hat{O}}{\hat{p}}$ is finite

Published on 15 Apr 2026 - 4:00

66

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How to show isomorphism between extension fields?

Published on 11 May 2026 - 9:44

691

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What is the history of the homomorphism concept?

Published on 10 May 2026 - 17:16

40

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If $W$ is a proper closed subset of $V$, then $W$ correspondes to a prime ideal.

Published on 15 Apr 2026 - 8:21

453

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What is $ \operatorname{Hom}_{k[x]}(k[x]/\langle x^2 \rangle , k[x]/ \langle x^3 \rangle ) $, where $ k $ is a field?

Published on 17 Apr 2026 - 6:41

282

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Determine $[F(\alpha) : F(\alpha^3)]$

Published on 16 Apr 2026 - 13:33

244

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For any field $K$, $t^3+xt+1$ is either irreducible or splits in $K$

Published on 15 Apr 2026 - 16:39

55

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Let $θ$ have minimal polynomial $t^3 +at^2 +bt +c$ over $\mathbb{Q}$. In what conditions in terms of $a,b,c$ $θ =φ^2$ where $φ ∈\mathbb{Q}(θ)$

Published on 14 Apr 2026 - 22:06

49

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Counterexamples between Rings and their polynomial Rings

Published on 14 Apr 2026 - 12:35

List Question

Field extensions isomorphic to subfields of each other

Divisibility conditions

What is Gal$_\mathbb{Q}(x^4 + 5x^3 + 10x + 5)$?

Pontryagin duality of finite groups

Finite field of with multiplication group isomorphic to the cyclic group of order $17$

$f (e_G )=e_H $ is necessary for Monoid homomorphisms

If $\hat{O}$ is compact, then $\frac{\hat{O}}{\hat{p}}$ is finite

How to show isomorphism between extension fields?

What is the history of the homomorphism concept?

If $W$ is a proper closed subset of $V$, then $W$ correspondes to a prime ideal.

What is $ \operatorname{Hom}_{k[x]}(k[x]/\langle x^2 \rangle , k[x]/ \langle x^3 \rangle ) $, where $ k $ is a field?

Determine $[F(\alpha) : F(\alpha^3)]$

For any field $K$, $t^3+xt+1$ is either irreducible or splits in $K$

Let $θ$ have minimal polynomial $t^3 +at^2 +bt +c$ over $\mathbb{Q}$. In what conditions in terms of $a,b,c$ $θ =φ^2$ where $φ ∈\mathbb{Q}(θ)$

Counterexamples between Rings and their polynomial Rings

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