Question

Group algebra is a free module of finite rank over any group sub-algebra

score 37 · Answer 1 · 2023-08-31 22:01:46

37

Views

Group algebra is a free module of finite rank over any group sub-algebra

Published on 31 Aug 2023 - 22:01

score 58 · Answer 2 · 2023-09-02 12:29:13

58

Views

Free module over a countable set

Published on 02 Sep 2023 - 12:29

score 261 · Answer 3 · 2026-03-25 16:06:44

261

Views

Every $K[G]$-module is torsionless?

Published on 25 Mar 2026 - 16:06

score 75 · Answer 4 · 2023-09-14 09:42:49

75

Views

Alternative proof for Structure theorem for finitely generated modules over a principal ideal domain

Published on 14 Sep 2023 - 9:42

score 50 · Answer 5 · 2026-03-28 01:48:49

50

Views

Finitely generated module equal to free module of rank $n$? Not just the quotient of free module.

Published on 28 Mar 2026 - 1:48

score 70 · Answer 6 · 2026-03-26 14:31:59

70

Views

Flatness of $\mathbb{C}[x_1,\ldots,x_n]$ over $\mathbb{C}[f]$, $f \in \mathbb{C}[x_1,\ldots,x_n]$, $n \geq 1$

Published on 26 Mar 2026 - 14:31

score 107 · Answer 7 · 2026-03-28 13:41:45

107

Views

Show that if $Q$ is a non-trivial $\mathbb{Z}$-module, that is divisible, then $Q$ can not be a projective $\mathbb{Z}$-module.

Published on 28 Mar 2026 - 13:41

score 128 · Answer 8 · 2023-10-01 23:50:50

128

Views

Standard decomposition of vector-space endomorphism as direct sum of abelian groups

Published on 01 Oct 2023 - 23:50

score 55 · Answer 9 · 2023-10-02 22:21:49

55

Views

When are the integers a free R-module?

Published on 02 Oct 2023 - 22:21

score 86 · Answer 10 · 2026-03-28 13:40:27

86

Views

$P$ is projective implies $P℘$ is a free $R℘$-module

Published on 28 Mar 2026 - 13:40

score 21 · Answer 11 · 2023-10-07 17:05:12

21

Views

Linear independence of a subset of elements in a finitely generated module to the number of generators of the module

Published on 07 Oct 2023 - 17:05

score 35 · Answer 12 · 2023-10-14 20:39:02

35

Views

When $R$-Module of Rank $r$ has a submodule isomorphic to $R^r$?

Published on 14 Oct 2023 - 20:39

score 53 · Answer 13 · 2023-10-28 08:49:49

53

Views

How to find an injective ring homomorphism from $S$ to $M_n(R)$,where S is a commutative unitary ring as well as a free module over its subring $R$?

Published on 28 Oct 2023 - 8:49

score 39 · Answer 14 · 2023-11-06 00:20:15

39

Views

Does this argument use the fact that $\{e_i\}$ is linearly independent at any point?

Published on 06 Nov 2023 - 0:20

score 117 · Answer 15 · 2023-11-11 10:05:25

117

Views

Are projective modules free over a polynomial ring with infinite indeterminates over a field?

Published on 11 Nov 2023 - 10:05

List Question

Group algebra is a free module of finite rank over any group sub-algebra

Free module over a countable set

Every $K[G]$-module is torsionless?

Alternative proof for Structure theorem for finitely generated modules over a principal ideal domain

Finitely generated module equal to free module of rank $n$? Not just the quotient of free module.

Flatness of $\mathbb{C}[x_1,\ldots,x_n]$ over $\mathbb{C}[f]$, $f \in \mathbb{C}[x_1,\ldots,x_n]$, $n \geq 1$

Show that if $Q$ is a non-trivial $\mathbb{Z}$-module, that is divisible, then $Q$ can not be a projective $\mathbb{Z}$-module.

Standard decomposition of vector-space endomorphism as direct sum of abelian groups

When are the integers a free R-module?

$P$ is projective implies $P℘$ is a free $R℘$-module

Linear independence of a subset of elements in a finitely generated module to the number of generators of the module

When $R$-Module of Rank $r$ has a submodule isomorphic to $R^r$?

How to find an injective ring homomorphism from $S$ to $M_n(R)$,where S is a commutative unitary ring as well as a free module over its subring $R$?

Does this argument use the fact that $\{e_i\}$ is linearly independent at any point?

Are projective modules free over a polynomial ring with infinite indeterminates over a field?

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