List questions from abstract-algebra

Published on 12 Apr 2026 - 16:30

127

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Let $F(X,Y,Z)=5X^2+3Y^2+8Z^2+6(YZ+ZX+XY)$. Find $(a,b,c) \in \mathbb{Z}^3$ not all divisible by $13$, such that $F(a,b,c)\equiv 0 \pmod{13^2}$.

Published on 14 Apr 2026 - 22:11

241

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Which of the following cannot be possible value for the number of elements of $G?$

Published on 15 Apr 2026 - 17:27

475

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composition of finite morphism

Published on 09 Apr 2026 - 11:07

586

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Geometric interpretation of the Noether normalization lemma

Published on 14 Apr 2026 - 9:44

579

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Why is a Nonzero Ideal of $\mathcal{O}_K$ Free of Rank $n$?

Published on 09 Apr 2026 - 0:33

104

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Property of homomorphism of groups

Published on 11 Apr 2026 - 5:06

344

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Universal Gröbner basis for $I = \left<x - y^nz \,\, | \,\, n \in \mathbb{N}\right>$

Published on 09 Apr 2026 - 0:05

51

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Multiplicatively Closed subset of universal enveloping algebra $U(\mathfrak{g})$ which is not left localisable

Published on 15 Apr 2026 - 9:04

801

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Example of a noetherian domain which is neither Dedekind domain nor UFD?

Published on 16 Apr 2026 - 10:32

102

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Geometry and equivalence of orbit spaces

Published on 14 Apr 2026 - 3:09

218

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Trying to understand a quotient of a polynomial ring

Published on 12 Apr 2026 - 5:10

234

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If A is a proper closed subalgebra of $C(X)$ ($X$ compact) and A $\subseteq I_{x_0}$ then $A = I_{x_0}$

Published on 14 Apr 2026 - 0:01

196

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Left-looking Gaussian elimination

Published on 10 Apr 2026 - 23:39

720

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Prove that Sym$\Omega$ is a group.

Published on 15 Apr 2026 - 15:12

List Question

How to express $(142536)$ as string of $(13456)$ and $(132)$ in $S_6$?

Let $F(X,Y,Z)=5X^2+3Y^2+8Z^2+6(YZ+ZX+XY)$. Find $(a,b,c) \in \mathbb{Z}^3$ not all divisible by $13$, such that $F(a,b,c)\equiv 0 \pmod{13^2}$.

Which of the following cannot be possible value for the number of elements of $G?$

composition of finite morphism

Geometric interpretation of the Noether normalization lemma

Why is a Nonzero Ideal of $\mathcal{O}_K$ Free of Rank $n$?

Property of homomorphism of groups

Universal Gröbner basis for $I = \left<x - y^nz \,\, | \,\, n \in \mathbb{N}\right>$

Multiplicatively Closed subset of universal enveloping algebra $U(\mathfrak{g})$ which is not left localisable

Example of a noetherian domain which is neither Dedekind domain nor UFD?

Geometry and equivalence of orbit spaces

Trying to understand a quotient of a polynomial ring

If A is a proper closed subalgebra of $C(X)$ ($X$ compact) and A $\subseteq I_{x_0}$ then $A = I_{x_0}$

Left-looking Gaussian elimination

Prove that Sym$\Omega$ is a group.

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