Question

Why is every element of a ring not a nilpotent?

score 143 · Answer 1 · 2023-09-25 12:27:03

143

Views

Why is every element of a ring not a nilpotent?

Published on 25 Sep 2023 - 12:27

score 49 · Answer 2 · 2023-09-29 14:48:05

49

Views

Extending the matrix property to nilpotent operators in infinite dimensional spaces.

Published on 29 Sep 2023 - 14:48

score 86 · Answer 3 · 2023-10-01 21:28:17

86

Views

If $A$ is nilpotent and $AB = A$, does $B$ have to be identity matrix?

Published on 01 Oct 2023 - 21:28

score 60 · Answer 4 · 2023-10-04 22:58:59

60

Views

In a ring $A$ such that $a^3=a$ $\forall a \in A$, determine the nilpotent elements of $A$.

Published on 04 Oct 2023 - 22:58

score 18 · Answer 5 · 2023-10-21 10:52:11

18

Views

Questions regarding the construction of nilpotent matrices in light of certain characteristics

Published on 21 Oct 2023 - 10:52

score 95 · Answer 6 · 2023-10-27 11:17:55

95

Views

Matrix with all off-diagonal elements equal 1

Published on 27 Oct 2023 - 11:17

score 82 · Answer 7 · 2023-11-02 18:41:13

82

Views

Are there any non-trivial nilpotent and idempotent in the ring $F[X,Y]/(X^2-Y^2)$, where $F$ is a field?

Published on 02 Nov 2023 - 18:41

score 60 · Answer 8 · 2023-11-21 14:42:56

60

Views

Algorithm and program for modelling a Free Nilpotent Lie algeabra

Published on 21 Nov 2023 - 14:42

score 127 · Answer 9 · 2023-11-27 19:43:50

127

Views

index of nilpotency of a linear transformation

Published on 27 Nov 2023 - 19:43

score 78 · Answer 10 · 2023-12-20 01:26:45

78

Views

Is the span of all nilpotent ideals also a nilpotent ideal?

Published on 20 Dec 2023 - 1:26

score 107 · Answer 11 · 2026-03-25 09:32:11

107

Views

Does $(x^2)(x^3) \neq 0$ imply $(x)(x^3) \neq 0$?

Published on 25 Mar 2026 - 9:32

score 130 · Answer 12 · 2024-01-16 15:05:27

130

Views

For nilpotent matrix $N$ over complex field, and for natural number $r$ show that there exists $A$ in $M_n(\mathbb{C})$ s.t. $A^r = N + I_n$

Published on 16 Jan 2024 - 15:05

score 70 · Answer 13 · 2024-01-23 16:18:55

70

Views

reduction of matrix (nilpotence)

Published on 23 Jan 2024 - 16:18

score 66 · Answer 14 · 2024-02-17 10:29:11

66

Views

If R is a ring with idempotent then eR is clean ring if and only if eRe is clean ring

Published on 17 Feb 2024 - 10:29

score 336 · Answer 15 · 2024-02-18 01:21:20

336

Views

Looking for a counterexample when dropping one of the constraints (Linear algebra)

Published on 18 Feb 2024 - 1:21

List Question

Why is every element of a ring not a nilpotent?

Extending the matrix property to nilpotent operators in infinite dimensional spaces.

If $A$ is nilpotent and $AB = A$, does $B$ have to be identity matrix?

In a ring $A$ such that $a^3=a$ $\forall a \in A$, determine the nilpotent elements of $A$.

Questions regarding the construction of nilpotent matrices in light of certain characteristics

Matrix with all off-diagonal elements equal 1

Are there any non-trivial nilpotent and idempotent in the ring $F[X,Y]/(X^2-Y^2)$, where $F$ is a field?

Algorithm and program for modelling a Free Nilpotent Lie algeabra

index of nilpotency of a linear transformation

Is the span of all nilpotent ideals also a nilpotent ideal?

Does $(x^2)(x^3) \neq 0$ imply $(x)(x^3) \neq 0$?

For nilpotent matrix $N$ over complex field, and for natural number $r$ show that there exists $A$ in $M_n(\mathbb{C})$ s.t. $A^r = N + I_n$

reduction of matrix (nilpotence)

If R is a ring with idempotent then eR is clean ring if and only if eRe is clean ring

Looking for a counterexample when dropping one of the constraints (Linear algebra)

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