List questions from abstract-algebra

Published on 13 Apr 2026 - 22:49

771

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Is there a notion of minimal polynomial if the ring is not a field?

Published on 11 May 2026 - 8:39

151

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How to prove that a Group $G$ with order $p^2$ must be a abelian group(where p is a prime)?

Published on 14 Apr 2026 - 17:52

171

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Factorization of polynomial in multiple variables by a root

Published on 13 Apr 2026 - 13:03

129

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Is there a correlation between the degree of an extension and it being an algebraic extension?

Published on 14 Apr 2026 - 6:42

313

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Finite extension with abelian Galois group

Published on 14 May 2026 - 7:42

64

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Linearly disjoint of local fields

Published on 12 Apr 2026 - 22:49

139

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In the ring $\mathbb{Z}[\sqrt{3}]=\{a+b\sqrt{3}\mid a,b \in \mathbb{Z}\}$, show the following.

Published on 13 Apr 2026 - 6:02

85

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Specific dimension calculation

Published on 11 Apr 2026 - 8:49

434

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Geometric interpretation of the roots of $\left(\frac{z-1}{1+i}\right)^{4} = -1+i$

Published on 10 May 2026 - 16:13

1.9k

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UFD iff PID in Dedekind domain.

Published on 15 Apr 2026 - 6:45

73

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Question about a comment on a different question. A rational root of a monic polynomial over $\Bbb Z[x]$ is an integer

Published on 09 Apr 2026 - 1:10

133

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Fundamental representations of $\mathfrak{gl}_3(\Bbb C)$

Published on 15 May 2026 - 19:50

77

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Preimage of ideal in $R/p$ for Dedekind ring $R$ and prime ideal $p$.

Published on 12 Apr 2026 - 20:53

550

Views

Sylow $2$-subgroup of ${\rm SL}(2,5)$

Published on 14 Apr 2026 - 19:38

List Question

Minimal subfield of two fields

Is there a notion of minimal polynomial if the ring is not a field?

How to prove that a Group $G$ with order $p^2$ must be a abelian group(where p is a prime)?

Factorization of polynomial in multiple variables by a root

Is there a correlation between the degree of an extension and it being an algebraic extension?

Finite extension with abelian Galois group

Linearly disjoint of local fields

In the ring $\mathbb{Z}[\sqrt{3}]=\{a+b\sqrt{3}\mid a,b \in \mathbb{Z}\}$, show the following.

Specific dimension calculation

Geometric interpretation of the roots of $\left(\frac{z-1}{1+i}\right)^{4} = -1+i$

UFD iff PID in Dedekind domain.

Question about a comment on a different question. A rational root of a monic polynomial over $\Bbb Z[x]$ is an integer

Fundamental representations of $\mathfrak{gl}_3(\Bbb C)$

Preimage of ideal in $R/p$ for Dedekind ring $R$ and prime ideal $p$.

Sylow $2$-subgroup of ${\rm SL}(2,5)$

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