Question

Show that $B^{(1)} = 0$ and $B^{(2)}$ have basis $\{[x_i,x_j]; i>j\}$

score 29 · Answer 1 · 2015-04-25 20:07:46

29

Views

Show that $B^{(1)} = 0$ and $B^{(2)}$ have basis $\{[x_i,x_j]; i>j\}$

Published on 25 Apr 2015 - 20:07

score 139 · Answer 2 · 2015-04-26 07:08:17

139

Views

Simple generator modules

Published on 26 Apr 2015 - 7:08

score 120 · Answer 3 · 2015-04-28 18:24:58

120

Views

torsion-free module and injective envelope of this

Published on 28 Apr 2015 - 18:24

score 159 · Answer 4 · 2015-04-29 18:29:36

159

Views

Are the isomorphism classes of simple left ideals in a semisimple ring finite?

Published on 29 Apr 2015 - 18:29

score 84 · Answer 5 · 2026-03-27 04:38:38

84

Views

On algebraicity of a formal power series

Published on 27 Mar 2026 - 4:38

score 1.1k · Answer 6 · 2015-04-30 04:29:44

1.1k

Views

Matrix Ring of a Semisimple Ring

Published on 30 Apr 2015 - 4:29

score 591 · Answer 7 · 2015-04-30 05:01:21

591

Views

Simple Artinian ring $S$ is isomorphic to a matrix ring over a division ring?

Published on 30 Apr 2015 - 5:01

score 300 · Answer 8 · 2015-04-30 05:19:35

300

Views

If $R/I$ and $R/J$ are semisimple, then so is $R/I\cap J$.

Published on 30 Apr 2015 - 5:19

score 123 · Answer 9 · 2026-03-28 06:00:30

123

Views

Conceptual approach to the formula $\sum_{i=1}^n \det(v_1, \ldots, Av_i, \ldots, v_n)=\text{tr}(A)\det(v_1, \ldots, v_n)$

Published on 28 Mar 2026 - 6:00

score 294 · Answer 10 · 2015-05-10 16:55:21

294

Views

Let $R$ a left artinian ring. Show that if $a \in R$ is not a right zero divisor, then $a$ is a unit in $R$.

Published on 10 May 2015 - 16:55

score 150 · Answer 11 · 2015-05-17 16:32:45

150

Views

Constant term of noncommutative $(X+Y+(XY)^{-1})^n$

Published on 17 May 2015 - 16:32

score 90 · Answer 12 · 2015-05-18 13:14:47

90

Views

If $I$ is a finitely generated semisimple left $R-$module, show that $I=Re$ for an idempotent $e \in I$.

Published on 18 May 2015 - 13:14

score 150 · Answer 13 · 2015-05-28 09:40:50

150

Views

Algebras $A_i$ generated by a single element over an infinite field, does $A_1 \times \cdots \times A_r$ has the same property?

Published on 28 May 2015 - 9:40

score 187 · Answer 14 · 2015-05-30 17:19:52

187

Views

Does $M_n(R_1)\cong M_n(R_2)$ imply $R_1\cong R_2$?

Published on 30 May 2015 - 17:19

score 167 · Answer 15 · 2015-06-01 18:42:54

167

Views

What is a formal model for equations in non-commutative ring?

Published on 01 Jun 2015 - 18:42

List Question

Show that $B^{(1)} = 0$ and $B^{(2)}$ have basis $\{[x_i,x_j]; i>j\}$

Simple generator modules

torsion-free module and injective envelope of this

Are the isomorphism classes of simple left ideals in a semisimple ring finite?

On algebraicity of a formal power series

Matrix Ring of a Semisimple Ring

Simple Artinian ring $S$ is isomorphic to a matrix ring over a division ring?

If $R/I$ and $R/J$ are semisimple, then so is $R/I\cap J$.

Conceptual approach to the formula $\sum_{i=1}^n \det(v_1, \ldots, Av_i, \ldots, v_n)=\text{tr}(A)\det(v_1, \ldots, v_n)$

Let $R$ a left artinian ring. Show that if $a \in R$ is not a right zero divisor, then $a$ is a unit in $R$.

Constant term of noncommutative $(X+Y+(XY)^{-1})^n$

If $I$ is a finitely generated semisimple left $R-$module, show that $I=Re$ for an idempotent $e \in I$.

Algebras $A_i$ generated by a single element over an infinite field, does $A_1 \times \cdots \times A_r$ has the same property?

Does $M_n(R_1)\cong M_n(R_2)$ imply $R_1\cong R_2$?

What is a formal model for equations in non-commutative ring?

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