List questions from noncommutative-algebra

Published on 26 Mar 2026 - 11:17

53

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Extension of semiprime ideals

Published on 29 Mar 2017 - 18:14

283

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$R$ and $R/radR$ have the same simple left modules.

Published on 02 Apr 2017 - 13:07

427

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$R$ is a prime right Goldie ring which contains a minimal right ideal. Show that $R$ must be a simple Artinian ring.

Published on 25 Mar 2026 - 6:06

232

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Idempotents of triangular matrix ring

Published on 09 Apr 2017 - 11:18

73

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Spectral triple for a (real) full matrix algebra

Published on 25 Mar 2026 - 20:34

141

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Example of a quasi nilpotent element which is not a nilpotent element

Published on 25 Mar 2026 - 14:22

90

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Meaning of "free on the basis"

Published on 19 Feb 2023 - 18:48

93

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Spectral triple on $\mathcal C(M)$ where $M$ is a compact Riemannian manifold, not necessarily spin

Published on 25 Mar 2026 - 16:03

17

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Power function in non-commutative algebras

Published on 14 Mar 2026 - 13:01

74

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Commuting operators vs. commutative rings, and localization in the quantum mechanical sense vs. commutative algebra sense.

Published on 29 Mar 2026 - 2:12

91

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How to define the non-commutative ring $\mathbb{F}_{4}+e\mathbb{F}_{4}$, $e^2=1$, $ae=ea^2$ in MAGMA(Computational Algebra System)?

Published on 23 Feb 2026 - 8:39

92

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Every $R$-module is injective implies $R$ is a product of simple rings

Published on 08 Mar 2023 - 18:03

39

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If $R$ is a product of matrix rings over division rings then every $R$ module is completely reducible

Published on 09 Mar 2023 - 13:22

86

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Ideals of the Lipschitz quaternions

Published on 10 Mar 2023 - 19:22

List Question

Nilpotent Radical is contained in the intersection of all prime ideals

Extension of semiprime ideals

$R$ and $R/radR$ have the same simple left modules.

$R$ is a prime right Goldie ring which contains a minimal right ideal. Show that $R$ must be a simple Artinian ring.

Idempotents of triangular matrix ring

Spectral triple for a (real) full matrix algebra

Example of a quasi nilpotent element which is not a nilpotent element

Meaning of "free on the basis"

Spectral triple on $\mathcal C(M)$ where $M$ is a compact Riemannian manifold, not necessarily spin

Power function in non-commutative algebras

Commuting operators vs. commutative rings, and localization in the quantum mechanical sense vs. commutative algebra sense.

How to define the non-commutative ring $\mathbb{F}_{4}+e\mathbb{F}_{4}$, $e^2=1$, $ae=ea^2$ in MAGMA(Computational Algebra System)?

Every $R$-module is injective implies $R$ is a product of simple rings

If $R$ is a product of matrix rings over division rings then every $R$ module is completely reducible

Ideals of the Lipschitz quaternions

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