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 48 · Answer 1 · 2019-12-13 13:44:35

48

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 13 Dec 2019 - 13:44

score 211 · Answer 2 · 2020-01-03 13:07:39

211

Views

Integral group ring of the free group on two generators

Published on 03 Jan 2020 - 13:07

score 131 · Answer 3 · 2020-01-11 23:15:08

131

Views

Exploring the isomorphisms of the group algebra $KG$

Published on 11 Jan 2020 - 23:15

score 99 · Answer 4 · 2020-01-13 21:18:37

99

Views

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

Published on 13 Jan 2020 - 21:18

score 169 · Answer 5 · 2020-02-12 09:21:05

169

Views

Inverse in a group ring

Published on 12 Feb 2020 - 9:21

score 210 · Answer 6 · 2020-03-11 16:29:32

210

Views

Invertibility in the Complex Group Ring

Published on 11 Mar 2020 - 16:29

score 325 · Answer 7 · 2020-03-12 14:05:24

325

Views

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

Published on 12 Mar 2020 - 14:05

score 684 · Answer 8 · 2020-04-13 12:12:25

684

Views

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

Published on 13 Apr 2020 - 12:12

score 239 · Answer 9 · 2020-04-14 15:25:41

239

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 14 Apr 2020 - 15:25

score 71 · Answer 10 · 2020-04-19 04:30:14

71

Views

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

Published on 19 Apr 2020 - 4:30

score 115 · Answer 11 · 2020-04-21 16:08:41

115

Views

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

Published on 21 Apr 2020 - 16:08

score 70 · Answer 12 · 2020-04-25 10:46:30

70

Views

Does every finite dimensional algebra contains a semisimple subalgebra?

Published on 25 Apr 2020 - 10:46

score 385 · Answer 13 · 2026-03-25 04:44:18

385

Views

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

Published on 25 Mar 2026 - 4:44

score 61 · Answer 14 · 2020-06-14 11:00:17

61

Views

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

Published on 14 Jun 2020 - 11:00

score 74 · Answer 15 · 2020-06-17 13:45:40

74

Views

Scalar extension of group algebras

Published on 17 Jun 2020 - 13:45

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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