List questions from nilpotence

Published on 05 Jan 2014 - 16:41

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$a+1,a-1$ invertible for nilpotent element

Published on 13 Jan 2014 - 22:01

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Nil-potency and similarity between matrices

Published on 18 Apr 2017 - 11:02

454

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Nilpotent linear map $x$ induces another nilpotent linear map $ \bar{x} : V/ U \rightarrow V/ U $ that has a basis that is strictly upper triangular.

Published on 20 Apr 2017 - 14:41

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Figuring out nilpotent $2 \times 2$ matrices

Published on 25 Apr 2017 - 15:56

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Prime Factorization and Nilpotents

Published on 26 Apr 2017 - 3:47

288

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An application of a criterion for nilpotent matrix

Published on 27 Apr 2017 - 14:03

197

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Identically vanishing polynomials in infinite commutative rings

Published on 01 May 2017 - 12:22

415

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General: Show a matrix is nilpotent.

Published on 02 May 2017 - 2:21

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Say $A^2 = 0$. Prove that for every real number $a$, the matrix $I + a A$ is invertible

Published on 02 May 2017 - 10:34

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Nilpotent with infinite degree?

Published on 04 May 2017 - 8:37

179

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If a commutative ring is connected, then its reduced ring is connected.

Published on 27 Mar 2026 - 8:41

546

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For a nilpotent operator $T^{n-1}=0 \iff dim(ker(T))\ge2$

Published on 04 May 2017 - 19:36

106

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How do I show that all of the chains in T's chain basis have the same length?

Published on 06 May 2017 - 12:59

442

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$f$ nilpotent and $\dim \ker f^k = \dim \ker f^{k+1}$ then $f^k=0$

Published on 06 May 2017 - 16:20

List Question

$ABAB=0_{n\times n}$, then must $BABA$ be $0_{n\times n}$?

$a+1,a-1$ invertible for nilpotent element

Nil-potency and similarity between matrices

Nilpotent linear map $x$ induces another nilpotent linear map $ \bar{x} : V/ U \rightarrow V/ U $ that has a basis that is strictly upper triangular.

Figuring out nilpotent $2 \times 2$ matrices

Prime Factorization and Nilpotents

An application of a criterion for nilpotent matrix

Identically vanishing polynomials in infinite commutative rings

General: Show a matrix is nilpotent.

Say $A^2 = 0$. Prove that for every real number $a$, the matrix $I + a A$ is invertible

Nilpotent with infinite degree?

If a commutative ring is connected, then its reduced ring is connected.

For a nilpotent operator $T^{n-1}=0 \iff dim(ker(T))\ge2$

How do I show that all of the chains in T's chain basis have the same length?

$f$ nilpotent and $\dim \ker f^k = \dim \ker f^{k+1}$ then $f^k=0$

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