Question

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

score 62 · Answer 1 · 2026-03-25 11:15:58

62

Views

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

Published on 25 Mar 2026 - 11:15

score 71 · Answer 2 · 2026-03-25 07:45:53

71

Views

Show that $\ker\sigma \subset \varphi_1(\ker\rho)$ and $\operatorname{im}\tau \subset \psi_2(\operatorname{im}\sigma)$.

Published on 25 Mar 2026 - 7:45

score 175 · Answer 3 · 2020-06-15 07:33:49

175

Views

Split extension of finite group and Sylow subgroup by $p$-group

Published on 15 Jun 2020 - 7:33

score 110 · Answer 4 · 2020-06-15 11:34:27

110

Views

Chain Complex morphism: Arbitrary maps instead of Homomorphism?

Published on 15 Jun 2020 - 11:34

score 459 · Answer 5 · 2020-06-15 15:56:00

459

Views

Weibel 2.5.1 Equivalent statements of injective $R$-module.

Published on 15 Jun 2020 - 15:56

score 178 · Answer 6 · 2026-02-23 08:42:19

178

Views

Hatcher Theorem 2.13 - is the subspace $X$ of its cone $CX$ a deformation retract of some neighborhood in $CX$?

Published on 23 Feb 2026 - 8:42

score 840 · Answer 7 · 2026-03-25 06:01:52

840

Views

Homotopy groups of quotient groups.

Published on 25 Mar 2026 - 6:01

score 39 · Answer 8 · 2020-06-23 14:36:41

39

Views

Show the induced sequence $A\otimes G \to B\otimes G\to C\otimes G \to 0$ is exact, how do we use the cokernel?

Published on 23 Jun 2020 - 14:36

score 130 · Answer 9 · 2020-06-23 20:35:33

130

Views

Constructing the inverse of a surjective homomorphism $g\otimes \operatorname{id}\colon B\otimes G \to C\otimes G$

Published on 23 Jun 2020 - 20:35

score 62 · Answer 10 · 2020-06-24 17:30:36

62

Views

Five term exact sequence - basis for the middle when I understand the rest?

Published on 24 Jun 2020 - 17:30

score 85 · Answer 11 · 2020-06-24 17:38:45

85

Views

Understand a quotient

Published on 24 Jun 2020 - 17:38

score 49 · Answer 12 · 2020-06-24 21:14:20

49

Views

Long exact sequence of reduced homology groups

Published on 24 Jun 2020 - 21:14

score 137 · Answer 13 · 2026-03-25 15:42:19

137

Views

Can two elements of an Ext group come from the same middle object of an SES?

Published on 25 Mar 2026 - 15:42

score 109 · Answer 14 · 2020-06-27 14:41:58

109

Views

Exact sequence and Vector Bundles on $\mathbb{P}^{n}$.

Published on 27 Jun 2020 - 14:41

score 21 · Answer 15 · 2020-06-27 16:41:07

21

Views

$Ra$ is a direct summand of M $\Leftrightarrow \exists f:M\rightarrow R$ an $R$-linear map such that $f(a)=1_R$

Published on 27 Jun 2020 - 16:41

List Question

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

Show that $\ker\sigma \subset \varphi_1(\ker\rho)$ and $\operatorname{im}\tau \subset \psi_2(\operatorname{im}\sigma)$.

Split extension of finite group and Sylow subgroup by $p$-group

Chain Complex morphism: Arbitrary maps instead of Homomorphism?

Weibel 2.5.1 Equivalent statements of injective $R$-module.

Hatcher Theorem 2.13 - is the subspace $X$ of its cone $CX$ a deformation retract of some neighborhood in $CX$?

Homotopy groups of quotient groups.

Show the induced sequence $A\otimes G \to B\otimes G\to C\otimes G \to 0$ is exact, how do we use the cokernel?

Constructing the inverse of a surjective homomorphism $g\otimes \operatorname{id}\colon B\otimes G \to C\otimes G$

Five term exact sequence - basis for the middle when I understand the rest?

Understand a quotient

Long exact sequence of reduced homology groups

Can two elements of an Ext group come from the same middle object of an SES?

Exact sequence and Vector Bundles on $\mathbb{P}^{n}$.

$Ra$ is a direct summand of M $\Leftrightarrow \exists f:M\rightarrow R$ an $R$-linear map such that $f(a)=1_R$

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