List questions from noncommutative-algebra

382

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Let $R = M_n(k)$, where $k$ is a field. Then any R-module that is finite dimensional over K is a direct sum of

Published on 14 Dec 2015 - 3:00

758

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Ring with Unique Simple Module

Published on 15 Dec 2015 - 17:42

624

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Augmentation ideal and the abelianization of $G$

Published on 28 Mar 2026 - 20:59

1.6k

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Compute the Jacobson radical of the group ring $\mathbb{F}_2S_3$.

Published on 26 Mar 2026 - 4:34

158

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Idempotent subideals of $J(R)$

Published on 02 Jan 2016 - 14:43

86

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A probable equality between two ideals

Published on 04 Jan 2016 - 4:26

243

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Idempotent direct summands of rings

Published on 04 Jan 2016 - 16:35

994

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Does the tensor product distribute over a direct sum exactly if all the involved modules are bimodules?

Published on 30 Mar 2026 - 1:51

438

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Idempotent ideals having only idempotents

Published on 31 Mar 2026 - 22:27

51

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Maximal right ideal of $\mathbb{H}[x]$

Published on 07 Jan 2016 - 23:01

1k

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Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)

Published on 09 Jan 2016 - 17:55

1k

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Examples of non-principal free ideals

Published on 09 Jan 2016 - 19:04

77

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Uncountably many left ideals?

Published on 28 Mar 2026 - 0:26

254

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A question about Semisimple ring and their Jacobson radical

Published on 20 Jan 2016 - 10:17

581

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If $e$ is idempotent and both $eRe$ and $(1-e)R(1-e)$ are orthogonally finite, is $R$ orthogonally finite?

Published on 21 Jan 2016 - 6:45

List Question

Let $R = M_n(k)$, where $k$ is a field. Then any R-module that is finite dimensional over K is a direct sum of

Ring with Unique Simple Module

Augmentation ideal and the abelianization of $G$

Compute the Jacobson radical of the group ring $\mathbb{F}_2S_3$.

Idempotent subideals of $J(R)$

A probable equality between two ideals

Idempotent direct summands of rings

Does the tensor product distribute over a direct sum exactly if all the involved modules are bimodules?

Idempotent ideals having only idempotents

Maximal right ideal of $\mathbb{H}[x]$

Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)

Examples of non-principal free ideals

Uncountably many left ideals?

A question about Semisimple ring and their Jacobson radical

If $e$ is idempotent and both $eRe$ and $(1-e)R(1-e)$ are orthogonally finite, is $R$ orthogonally finite?

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