Question

Why quotient of free $\mathbb{Z}F$-module can be seen as a free module on $\mathbb{Z}G$, where $G$ is a quotient of $F$?

score 50 · Answer 1 · 2026-04-14 21:29:26

50

Views

Why quotient of free $\mathbb{Z}F$-module can be seen as a free module on $\mathbb{Z}G$, where $G$ is a quotient of $F$?

Published on 14 Apr 2026 - 21:29

score 214 · Answer 2 · 2026-04-11 05:14:17

214

Views

Integral group ring of the free group on two generators

Published on 11 Apr 2026 - 5:14

score 132 · Answer 3 · 2026-03-25 12:49:17

132

Views

Exploring the isomorphisms of the group algebra $KG$

Published on 25 Mar 2026 - 12:49

score 102 · Answer 4 · 2026-04-14 15:25:45

102

Views

Is $\Bbb{Q}[F]$ a field whenever $F$ is a field?

Published on 14 Apr 2026 - 15:25

score 173 · Answer 5 · 2026-04-30 15:18:02

173

Views

Inverse in a group ring

Published on 30 Apr 2026 - 15:18

score 213 · Answer 6 · 2026-04-12 12:36:13

213

Views

Invertibility in the Complex Group Ring

Published on 12 Apr 2026 - 12:36

score 328 · Answer 7 · 2026-04-13 19:59:57

328

Views

Szamuely's "Galois groups and fundamental groups" exercise I.7

Published on 13 Apr 2026 - 19:59

score 687 · Answer 8 · 2026-04-14 22:29:04

687

Views

Why is the constant term of $(1+x+y+xy)^n$ equal to $\frac{1}{2}\binom{2n}{n}$？

Published on 14 Apr 2026 - 22:29

score 243 · Answer 9 · 2026-05-10 17:02:39

243

Views

Let $x^2=y^2=1$ and $xy\neq yx$. There are $\binom{2n}{n}$ expressions of length $2n$ in $x$ and $y$ that are equal to $1$.

Published on 10 May 2026 - 17:02

score 74 · Answer 10 · 2026-04-16 09:29:21

74

Views

Dimension of center of k[G]/rad k[G] where characteristic of k divides the order of G.

Published on 16 Apr 2026 - 9:29

score 118 · Answer 11 · 2026-04-16 05:26:21

118

Views

Structure of ideals in $\mathbb{F}_q[G]$

Published on 16 Apr 2026 - 5:26

score 73 · Answer 12 · 2026-04-15 12:47:17

73

Views

Does every finite dimensional algebra contains a semisimple subalgebra?

Published on 15 Apr 2026 - 12:47

score 388 · Answer 13 · 2026-05-11 01:12:56

388

Views

The category of finite dimensional right $KG$-modules is equivalent to the category of finite dimensional representations of a quiver $Q$

Published on 11 May 2026 - 1:12

score 66 · Answer 14 · 2026-04-16 16:44:51

66

Views

How to show $\operatorname{Ext}^1(I, \mathbb{Z})\cong\mathbb{Z}/2$ for $\mathbb{Z}[C_2]$?

Published on 16 Apr 2026 - 16:44

score 77 · Answer 15 · 2026-04-11 19:29:50

77

Views

Scalar extension of group algebras

Published on 11 Apr 2026 - 19:29

List Question

Why quotient of free $\mathbb{Z}F$-module can be seen as a free module on $\mathbb{Z}G$, where $G$ is a quotient of $F$?

Integral group ring of the free group on two generators

Exploring the isomorphisms of the group algebra $KG$

Is $\Bbb{Q}[F]$ a field whenever $F$ is a field?

Inverse in a group ring

Invertibility in the Complex Group Ring

Szamuely's "Galois groups and fundamental groups" exercise I.7

Why is the constant term of $(1+x+y+xy)^n$ equal to $\frac{1}{2}\binom{2n}{n}$？

Let $x^2=y^2=1$ and $xy\neq yx$. There are $\binom{2n}{n}$ expressions of length $2n$ in $x$ and $y$ that are equal to $1$.

Dimension of center of k[G]/rad k[G] where characteristic of k divides the order of G.

Structure of ideals in $\mathbb{F}_q[G]$

Does every finite dimensional algebra contains a semisimple subalgebra?

The category of finite dimensional right $KG$-modules is equivalent to the category of finite dimensional representations of a quiver $Q$

How to show $\operatorname{Ext}^1(I, \mathbb{Z})\cong\mathbb{Z}/2$ for $\mathbb{Z}[C_2]$?

Scalar extension of group algebras

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