Question

Given a representation $\phi: L \rightarrow \mathfrak {gl}(V)$ $\phi(L)$ in End $V$ leaves invariant precisely the same subspaces as $L$.

score 74 · Answer 1 · 2026-03-20 03:13:15

Given a representation $\phi: L \rightarrow \mathfrak {gl}(V)$ $\phi(L)$ in End $V$ leaves invariant precisely the same subspaces as $L$.

score 25 · Answer 2 · 2018-01-17 17:22:06

25

Views

Examples of an Abel group and a ring such that module can not be formed.

Published on 17 Jan 2018 - 17:22

score 244 · Answer 3 · 2026-03-22 21:35:38

244

Views

Showing that $ \text{Ind}_H^G W \cong \text{Ind}_K^G(\text{Ind}_H^K W)$

Published on 22 Mar 2026 - 21:35

score 335 · Answer 4 · 2026-03-20 00:55:22

335

Views

Localization of a non-zero module is non-zero?

Published on 20 Mar 2026 - 0:55

score 361 · Answer 5 · 2026-03-19 23:14:18

361

Views

Relation between profinite abelian groups and $\hat{\Bbb{Z}}$ modules

Published on 19 Mar 2026 - 23:14

score 559 · Answer 6 · 2026-03-22 14:16:04

559

Views

Colimit of a directed system of modules

Published on 22 Mar 2026 - 14:16

score 518 · Answer 7 · 2026-03-24 13:57:30

518

Views

Proposition 3.7 in Atiyah-Macdonald (Tensor product of fractions is fraction of tensor product)

Published on 24 Mar 2026 - 13:57

score 1.1k · Answer 8 · 2026-03-23 08:51:05

1.1k

Views

Flat modules over a PID

Published on 23 Mar 2026 - 8:51

score 857 · Answer 9 · 2026-03-17 19:18:13

857

Views

A sequence is exact iff the corresponding sequence is exact

Published on 17 Mar 2026 - 19:18

score 88 · Answer 10 · 2026-03-25 02:56:52

88

Views

Module and Ring

Published on 25 Mar 2026 - 2:56

score 93 · Answer 11 · 2026-03-22 12:58:49

93

Views

Exponentiation property of the modulo operator

Published on 22 Mar 2026 - 12:58

score 99 · Answer 12 · 2026-03-24 22:01:38

99

Views

$L = \mathfrak{sl}(2,F)$: Viewing $M = \mathfrak{sl}(3,F)$ as an $L$-module.

Published on 24 Mar 2026 - 22:01

score 553 · Answer 13 · 2026-03-25 04:37:47

553

Views

Every finitely generated $R$-module has simple quotient

Published on 25 Mar 2026 - 4:37

score 89 · Answer 14 · 2026-03-25 04:40:40

89

Views

$\bigoplus_{i=1}^\infty\mathbb{Z}\not\cong\prod_{i=1}^\infty\mathbb{Z}$

Published on 25 Mar 2026 - 4:40

score 74 · Answer 15 · 2026-03-23 02:47:55

74

Views

Projectivity of a module

Published on 23 Mar 2026 - 2:47

List Question

Given a representation $\phi: L \rightarrow \mathfrak {gl}(V)$ $\phi(L)$ in End $V$ leaves invariant precisely the same subspaces as $L$.

Examples of an Abel group and a ring such that module can not be formed.

Showing that $ \text{Ind}_H^G W \cong \text{Ind}_K^G(\text{Ind}_H^K W)$

Localization of a non-zero module is non-zero?

Relation between profinite abelian groups and $\hat{\Bbb{Z}}$ modules

Colimit of a directed system of modules

Proposition 3.7 in Atiyah-Macdonald (Tensor product of fractions is fraction of tensor product)

Flat modules over a PID

A sequence is exact iff the corresponding sequence is exact

Module and Ring

Exponentiation property of the modulo operator

$L = \mathfrak{sl}(2,F)$: Viewing $M = \mathfrak{sl}(3,F)$ as an $L$-module.

Every finitely generated $R$-module has simple quotient

$\bigoplus_{i=1}^\infty\mathbb{Z}\not\cong\prod_{i=1}^\infty\mathbb{Z}$

Projectivity of a module

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