List questions from abstract-algebra

Published on 10 Apr 2026 - 2:57

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When people say "an algebra" do they always mean "an algebra over a field"?

Published on 09 Apr 2026 - 9:42

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Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Published on 10 Apr 2026 - 12:30

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Why does $|G/H|=|G|/|H|$?

Published on 31 Mar 2026 - 23:36

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Discriminant of $X^n+pX+q$

Published on 09 Apr 2026 - 0:55

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Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.

Published on 08 Apr 2026 - 22:26

105

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Abelian group proof

Published on 05 Apr 2026 - 16:01

133

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Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective

Published on 08 Apr 2026 - 22:44

107

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How to show that $\mathbb{Z}_5[i] = \{a + bi:a,b\in\mathbb{Z}_5 \}$ is a ring.

Published on 15 Jan 2018 - 23:27

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Exercise 15.10 in Cox's Book (first part)

Published on 08 Apr 2026 - 20:59

323

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In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?

Published on 09 Apr 2026 - 0:32

256

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Ring of remainders definition

Published on 09 Apr 2026 - 1:23

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The number of conjugacy classes of a finite group

Published on 08 Apr 2026 - 22:28

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Prove that there is no subgroup of index $6$ in a simple group of order $240$

Published on 09 Apr 2026 - 2:01

530

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The subgroup of upper triangular matrices of $GL_n(F)$ is equal to its normalizer

Published on 16 Jan 2018 - 6:13

List Question

Isomorphism of irreducible R-modules

When people say "an algebra" do they always mean "an algebra over a field"?

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Why does $|G/H|=|G|/|H|$?

Discriminant of $X^n+pX+q$

Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.

Abelian group proof

Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective

How to show that $\mathbb{Z}_5[i] = \{a + bi:a,b\in\mathbb{Z}_5 \}$ is a ring.

Exercise 15.10 in Cox's Book (first part)

In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?

Ring of remainders definition

The number of conjugacy classes of a finite group

Prove that there is no subgroup of index $6$ in a simple group of order $240$

The subgroup of upper triangular matrices of $GL_n(F)$ is equal to its normalizer

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