List questions from noncommutative-algebra

Published on 30 Mar 2026 - 8:14

67

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In a ring $1+\epsilon+\cdots+\epsilon^{p-1}=0$ implies $1+\epsilon^c+\epsilon^{2c}+\cdots+\epsilon^{(p-1)c}=0$ for $0<c<p$.

Published on 29 Feb 2024 - 9:56

24

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Is the Eigen spectrum of a matrix completely defined by the algebra of its parts?

Published on 26 Mar 2026 - 12:37

39

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Non commutative field of characteristic $\neq 0$

Published on 13 Mar 2024 - 12:34

73

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Inverse of a 2x2 quaternion matrix: whence this formula?

Published on 15 Mar 2024 - 0:06

69

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Non commutative Non reduced ring

Published on 16 Mar 2024 - 20:20

39

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Comultiplication on the tensor algebra

Published on 25 Mar 2026 - 23:35

29

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Does this property generalize to modules over noncommutative rings?

Published on 17 Mar 2024 - 19:53

47

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To what extent are submodules of $R^n$, for a ring $R$, describable by systems of linear equations?

Published on 17 Mar 2024 - 23:16

30

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Lie algebra cohomology of formal non-commutative vector fields

Published on 23 Feb 2026 - 4:40

30

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Two algebra structures on endomorphisms

Published on 19 Mar 2024 - 20:54

57

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Using Bergman's Diamond Lemma to prove a PBW theorem

Published on 22 Mar 2024 - 16:20

52

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How to prove when $R$ is not a commutative ring, $M\otimes_R N$ is not a module

Published on 24 Mar 2024 - 11:01

67

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Is there always an automorphism distinct from identity in a simple module?

Published on 25 Mar 2024 - 0:52

600

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Simple $R$-modules are isomorphic

Published on 05 Jan 2015 - 8:50

List Question

Fixed points of automorphism over quaternions

In a ring $1+\epsilon+\cdots+\epsilon^{p-1}=0$ implies $1+\epsilon^c+\epsilon^{2c}+\cdots+\epsilon^{(p-1)c}=0$ for $0<c<p$.

Is the Eigen spectrum of a matrix completely defined by the algebra of its parts?

Non commutative field of characteristic $\neq 0$

Inverse of a 2x2 quaternion matrix: whence this formula?

Non commutative Non reduced ring

Comultiplication on the tensor algebra

Does this property generalize to modules over noncommutative rings?

To what extent are submodules of $R^n$, for a ring $R$, describable by systems of linear equations?

Lie algebra cohomology of formal non-commutative vector fields

Two algebra structures on endomorphisms

Using Bergman's Diamond Lemma to prove a PBW theorem

How to prove when $R$ is not a commutative ring, $M\otimes_R N$ is not a module

Is there always an automorphism distinct from identity in a simple module?

Simple $R$-modules are isomorphic

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