Question

If a unit and nilpotent element commute in a ring, their sum is also a unit.

score 669 · Answer 1 · 2017-01-20 01:33:17

669

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If a unit and nilpotent element commute in a ring, their sum is also a unit.

Published on 20 Jan 2017 - 1:33

score 419 · Answer 2 · 2017-01-20 08:24:06

419

Views

If $1-x$ is a ring unit then is this ring nilpotent?

Published on 20 Jan 2017 - 8:24

score 39 · Answer 3 · 2017-01-31 10:26:51

39

Views

In class $2$ nilpotent groups, does $[G:HZ]<\infty$ imply $[G:H]<\infty$?

Published on 31 Jan 2017 - 10:26

score 543 · Answer 4 · 2017-02-03 06:14:39

543

Views

If $S=R/Nil(R)$ is a quotient ring then $Nil(S)=\{0_s\}$

Published on 03 Feb 2017 - 6:14

score 891 · Answer 5 · 2026-03-25 13:34:20

891

Views

Let $R$ be a commutative ring with unity of prime characteristic $p$. If $a\in R$ is nilpotent then is $1+a$ unipotent?

Published on 25 Mar 2026 - 13:34

score 1.7k · Answer 6 · 2017-02-12 22:04:12

1.7k

Views

Strictly Upper Triangular $n\times n$ Matrices form a Nilpotent Lie Algebra over $\mathbb{C}$ for $n\geq 2$

Published on 12 Feb 2017 - 22:04

score 108 · Answer 7 · 2017-02-22 14:21:06

108

Views

nilpotent elements in $\Bbb Z_n[i]$

Published on 22 Feb 2017 - 14:21

score 2.2k · Answer 8 · 2017-02-23 22:47:30

2.2k

Views

Does there exist a $2×2$ matrix such that $A^2 \neq 0$ but $A^3=0$?

Published on 23 Feb 2017 - 22:47

score 211 · Answer 9 · 2017-03-01 15:52:47

211

Views

Nilpotent elements in $\mathbb Z_n$

Published on 01 Mar 2017 - 15:52

score 122 · Answer 10 · 2017-03-03 02:34:54

122

Views

Rank of a special matrix

Published on 03 Mar 2017 - 2:34

score 135 · Answer 11 · 2017-03-03 15:36:37

135

Views

Nilpotency rank

Published on 03 Mar 2017 - 15:36

score 97 · Answer 12 · 2017-03-05 22:58:40

97

Views

Argument verification $f = a_0 + ... + a_nx^n$ in $A[x]$ is nilpotent iff $a_0,...,a_n$ is nilpotent.

Published on 05 Mar 2017 - 22:58

score 1.4k · Answer 13 · 2017-03-06 04:54:16

1.4k

Views

Nilpotent Matrix is Similar to a block diagonal matrix

Published on 06 Mar 2017 - 4:54

score 57 · Answer 14 · 2017-03-07 05:08:10

57

Views

Questions about nilpotence in commutative rings and zero divisors

Published on 07 Mar 2017 - 5:08

score 392 · Answer 15 · 2017-03-21 21:06:05

392

Views

Example of ring satisfying nilpotent condition

Published on 21 Mar 2017 - 21:06

List Question

If a unit and nilpotent element commute in a ring, their sum is also a unit.

If $1-x$ is a ring unit then is this ring nilpotent?

In class $2$ nilpotent groups, does $[G:HZ]<\infty$ imply $[G:H]<\infty$?

If $S=R/Nil(R)$ is a quotient ring then $Nil(S)=\{0_s\}$

Let $R$ be a commutative ring with unity of prime characteristic $p$. If $a\in R$ is nilpotent then is $1+a$ unipotent?

Strictly Upper Triangular $n\times n$ Matrices form a Nilpotent Lie Algebra over $\mathbb{C}$ for $n\geq 2$

nilpotent elements in $\Bbb Z_n[i]$

Does there exist a $2×2$ matrix such that $A^2 \neq 0$ but $A^3=0$?

Nilpotent elements in $\mathbb Z_n$

Rank of a special matrix

Nilpotency rank

Argument verification $f = a_0 + ... + a_nx^n$ in $A[x]$ is nilpotent iff $a_0,...,a_n$ is nilpotent.

Nilpotent Matrix is Similar to a block diagonal matrix

Questions about nilpotence in commutative rings and zero divisors

Example of ring satisfying nilpotent condition

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