List questions from abstract-algebra

179

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Prove that $\alpha^2-3\alpha+1$ is not in the ideal $(5,\alpha+2)$ in $\mathbb{Z[\alpha]}$ where $\alpha=2^{1/3}$

Published on 16 Apr 2026 - 10:01

125

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Localization of Modules over Dedekind domains

Published on 18 Apr 2026 - 15:22

77

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Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

Published on 16 Apr 2026 - 4:54

65

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$R$ is integral domain

Published on 10 Apr 2026 - 15:18

46

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Prove isomorphism 0f quotient.

Published on 15 Apr 2026 - 5:21

94

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How to show $\frac{M_1 \oplus M´}{M_1} \simeq \frac{N_1 \oplus N´}{N_1} $ if we know $M´ \simeq N´$?

Published on 15 Apr 2026 - 17:49

83

Views

Group of order $4$ such that $x^2=1$ for all $x$?

Published on 17 Apr 2026 - 0:48

88

Views

Generalized Heisenberg algebras

Published on 12 Apr 2026 - 9:21

420

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Product of solutions of quadratic equations equal constant term

Published on 11 Apr 2026 - 14:03

63

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Abstract Algebra - define and find kernal of homomorphism from $\mathbb Q[x]$ to $\mathbb Q[\sqrt2]$

Published on 14 Apr 2026 - 22:19

157

Views

Counting elements of a particular order in Dihedral groups

Published on 12 Apr 2026 - 14:52

38

Views

Determine Gal (K/P)

Published on 15 Apr 2026 - 6:49

486

Views

Matrix Ring over Semisimple Ring

Published on 14 Apr 2026 - 19:59

1.9k

Views

Reference for group cohomology

Published on 14 Apr 2026 - 21:12

193

Views

Profinite completion of integers

Published on 20 Apr 2026 - 17:21

List Question

Prove that $\alpha^2-3\alpha+1$ is not in the ideal $(5,\alpha+2)$ in $\mathbb{Z[\alpha]}$ where $\alpha=2^{1/3}$

Localization of Modules over Dedekind domains

Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

$R$ is integral domain

Prove isomorphism 0f quotient.

How to show $\frac{M_1 \oplus M´}{M_1} \simeq \frac{N_1 \oplus N´}{N_1} $ if we know $M´ \simeq N´$?

Group of order $4$ such that $x^2=1$ for all $x$?

Generalized Heisenberg algebras

Product of solutions of quadratic equations equal constant term

Abstract Algebra - define and find kernal of homomorphism from $\mathbb Q[x]$ to $\mathbb Q[\sqrt2]$

Counting elements of a particular order in Dihedral groups

Determine Gal (K/P)

Matrix Ring over Semisimple Ring

Reference for group cohomology

Profinite completion of integers

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