Question

For a ring $R$, if all left $R$-modules are semisimple, then all short exact sequences of left $R$-modules split.

score 1k · Answer 1 · 2017-01-31 19:50:14

1k

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For a ring $R$, if all left $R$-modules are semisimple, then all short exact sequences of left $R$-modules split.

Published on 31 Jan 2017 - 19:50

score 143 · Answer 2 · 2017-02-02 20:53:50

143

Views

faithful semisimple modules

Published on 02 Feb 2017 - 20:53

score 1.6k · Answer 3 · 2017-02-04 17:17:16

1.6k

Views

A Jacobson radical of a matrix ring

Published on 04 Feb 2017 - 17:17

score 196 · Answer 4 · 2026-03-26 12:52:00

196

Views

Tensor products and intersections in non-commutative setting

Published on 26 Mar 2026 - 12:52

score 219 · Answer 5 · 2026-03-25 07:43:08

219

Views

Showing an isomorphism of $R[G]$-modules using the regular representation

Published on 25 Mar 2026 - 7:43

score 35 · Answer 6 · 2017-02-11 15:10:56

35

Views

Let $I, M$ be proper idelas of a ring $R$. Prove the following:

Published on 11 Feb 2017 - 15:10

score 204 · Answer 7 · 2017-02-12 20:12:29

204

Views

Let $I$ be left ideal and $J$ be two-sided ideal in $R$. Prove if $I, J$ are nil then $I + J$ is nil left ideal.

Published on 12 Feb 2017 - 20:12

score 135 · Answer 8 · 2017-02-15 10:58:19

135

Views

Is the intersection of the kernels of all the linear forms trivial?

Published on 15 Feb 2017 - 10:58

score 137 · Answer 9 · 2017-02-15 21:44:54

137

Views

Is an element in a module that is annihilated by all the scalars necessarily zero?

Published on 15 Feb 2017 - 21:44

score 100 · Answer 10 · 2017-02-18 04:06:49

100

Views

Minimal Ideals of Corner Rings

Published on 18 Feb 2017 - 4:06

score 719 · Answer 11 · 2017-02-20 07:18:41

719

Views

Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.

Published on 20 Feb 2017 - 7:18

score 43 · Answer 12 · 2017-02-20 09:23:40

43

Views

Is there any finite groups with no subgroup for one and only one divisor of order of G of index greater than 2.

Published on 20 Feb 2017 - 9:23

score 54 · Answer 13 · 2017-02-20 16:37:05

54

Views

Example of finite groups with no subgroup for only one d such that $d | d_1$ and G has proper subgroup of order $d_1$.

Published on 20 Feb 2017 - 16:37

score 1.5k · Answer 14 · 2017-02-20 19:34:51

1.5k

Views

Every Submodule of a Free Module is Isomorphic to a Direct Sum of Ideals

Published on 20 Feb 2017 - 19:34

score 158 · Answer 15 · 2017-02-21 06:31:09

158

Views

How can I find all rings with 8 elements such that they do not have any nilpotent elements?

Published on 21 Feb 2017 - 6:31

List Question

For a ring $R$, if all left $R$-modules are semisimple, then all short exact sequences of left $R$-modules split.

faithful semisimple modules

A Jacobson radical of a matrix ring

Tensor products and intersections in non-commutative setting

Showing an isomorphism of $R[G]$-modules using the regular representation

Let $I, M$ be proper idelas of a ring $R$. Prove the following:

Let $I$ be left ideal and $J$ be two-sided ideal in $R$. Prove if $I, J$ are nil then $I + J$ is nil left ideal.

Is the intersection of the kernels of all the linear forms trivial?

Is an element in a module that is annihilated by all the scalars necessarily zero?

Minimal Ideals of Corner Rings

Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.

Is there any finite groups with no subgroup for one and only one divisor of order of G of index greater than 2.

Example of finite groups with no subgroup for only one d such that $d | d_1$ and G has proper subgroup of order $d_1$.

Every Submodule of a Free Module is Isomorphic to a Direct Sum of Ideals

How can I find all rings with 8 elements such that they do not have any nilpotent elements?

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