List questions from nilpotence

Published on 10 Apr 2023 - 2:58

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Is the only possible multiplicative structure on a finite dimensional vector space that of a product ring of finite field extensions?

Published on 25 Apr 2023 - 20:57

56

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Is every solvable algebras are nilpotent?

Published on 26 Mar 2026 - 1:53

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Proving an algebra is nilpotent

Published on 25 Mar 2026 - 9:23

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Prove that the following statements are equivalent.

Published on 25 Mar 2026 - 23:37

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Let $A$ and $B$ be nilpotent $n \times n$ matrices with $AB = BA$. Show that $A + B$ is also nilpotent.

Published on 13 May 2023 - 13:45

150

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Nilpotent elements in a quotient of a polynomial ring.

Published on 21 May 2023 - 13:25

100

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How to prove that $2A+B^2$ is nilpotent matrix

Published on 22 May 2023 - 14:01

40

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There is $f$ nonnilpotent in $A[[x]]$ with nilpotent coefficients -- solution verification

Published on 22 May 2023 - 16:53

13

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conditions for an algebra generated by idempotents to be solvable/nilpotent

Published on 13 Jun 2023 - 9:45

112

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Nilpotent, upper triangular sum and product of matrices

Published on 12 Jul 2023 - 8:50

370

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Prove if $M^2 =0$, then $\operatorname{rank}(M+M^T)=2\operatorname{rank}(M)$.

Published on 25 Jul 2023 - 14:55

103

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Given a nilpotent matrix $A$ of index 3, prove that its transpose $A^T$ is also nilpotent of index 3

Published on 05 Aug 2023 - 11:55

37

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How to prove this Lie algebra is nilpotent?

Published on 23 Aug 2023 - 4:04

40

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Nilpotence of a linear endomorphism

Published on 23 Sep 2023 - 11:50

List Question

Nilpotent operator over even dimension real vector space

Is the only possible multiplicative structure on a finite dimensional vector space that of a product ring of finite field extensions?

Is every solvable algebras are nilpotent?

Proving an algebra is nilpotent

Prove that the following statements are equivalent.

Let $A$ and $B$ be nilpotent $n \times n$ matrices with $AB = BA$. Show that $A + B$ is also nilpotent.

Nilpotent elements in a quotient of a polynomial ring.

How to prove that $2A+B^2$ is nilpotent matrix

There is $f$ nonnilpotent in $A[[x]]$ with nilpotent coefficients -- solution verification

conditions for an algebra generated by idempotents to be solvable/nilpotent

Nilpotent, upper triangular sum and product of matrices

Prove if $M^2 =0$, then $\operatorname{rank}(M+M^T)=2\operatorname{rank}(M)$.

Given a nilpotent matrix $A$ of index 3, prove that its transpose $A^T$ is also nilpotent of index 3

How to prove this Lie algebra is nilpotent?

Nilpotence of a linear endomorphism

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