Question

Let $A$ and $B$ be nilpotent matrices that commute with $[A,B]$. If $A$, $B$, and $[A,B]$ are all nilpotent, show that $A+B$ is nilpotent.

score 1.3k · Answer 1 · 2026-03-25 12:28:17

1.3k

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Let $A$ and $B$ be nilpotent matrices that commute with $[A,B]$. If $A$, $B$, and $[A,B]$ are all nilpotent, show that $A+B$ is nilpotent.

Published on 25 Mar 2026 - 12:28

score 96 · Answer 2 · 2018-11-21 23:41:50

96

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product of ideals in matrix ring

Published on 21 Nov 2018 - 23:41

score 47 · Answer 3 · 2018-11-22 02:59:42

47

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What are S-integral matrices for S a finite set of primes in a number field?

Published on 22 Nov 2018 - 2:59

score 313 · Answer 4 · 2018-11-22 07:28:42

313

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Which polynomial gcd is "correct"? [unit normalization of GCDs]

Published on 22 Nov 2018 - 7:28

score 60 · Answer 5 · 2026-03-30 05:15:27

60

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On showing that $\varphi(N)=(N+K)/K$, for modules $N,K<M$, $\varphi$ natural map.

Published on 30 Mar 2026 - 5:15

score 353 · Answer 6 · 2018-11-22 18:17:29

353

Views

Prove that $(H,+,\circ)$ is unital commutative ring.

Published on 22 Nov 2018 - 18:17

score 240 · Answer 7 · 2026-03-25 04:35:35

240

Views

Field Extensions and Injectivity

Published on 25 Mar 2026 - 4:35

score 265 · Answer 8 · 2026-03-25 04:40:55

265

Views

How to prove that $Ф(1) = 1'$ if $R'$ is an integral domain?

Published on 25 Mar 2026 - 4:40

score 36 · Answer 9 · 2018-11-24 03:12:05

36

Views

Show that $Z(I_{A})=A$

Published on 24 Nov 2018 - 3:12

score 94 · Answer 10 · 2018-11-24 03:34:24

94

Views

Show that $I_{Z(I)}=I$

Published on 24 Nov 2018 - 3:34

score 1.6k · Answer 11 · 2018-11-24 16:39:55

1.6k

Views

Find all Ring homomorphisms of $f: \mathbb Q\to \mathbb Q$

Published on 24 Nov 2018 - 16:39

score 83 · Answer 12 · 2026-03-25 01:18:40

$G$ finite group and $\mathbb{C}[G]$ its group ring, show: $K_i = \sum_{a_k\in cl_G(a_i)} a_k $, then $Z(\mathbb{C}[G])=span_\mathbb{C}(K_1,...,K_n)$

score 244 · Answer 13 · 2026-03-25 17:43:56

244

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Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Published on 25 Mar 2026 - 17:43

score 25 · Answer 14 · 2026-03-29 19:45:49

25

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Checking Ideals of Rings

Published on 29 Mar 2026 - 19:45

score 219 · Answer 15 · 2018-11-25 03:55:11

219

Views

Find integer solutions of $xy=-1$ (using only elementary ring theory).

Published on 25 Nov 2018 - 3:55

List Question

Let $A$ and $B$ be nilpotent matrices that commute with $[A,B]$. If $A$, $B$, and $[A,B]$ are all nilpotent, show that $A+B$ is nilpotent.

product of ideals in matrix ring

What are S-integral matrices for S a finite set of primes in a number field?

Which polynomial gcd is "correct"? [unit normalization of GCDs]

On showing that $\varphi(N)=(N+K)/K$, for modules $N,K<M$, $\varphi$ natural map.

Prove that $(H,+,\circ)$ is unital commutative ring.

Field Extensions and Injectivity

How to prove that $Ф(1) = 1'$ if $R'$ is an integral domain?

Show that $Z(I_{A})=A$

Show that $I_{Z(I)}=I$

Find all Ring homomorphisms of $f: \mathbb Q\to \mathbb Q$

$G$ finite group and $\mathbb{C}[G]$ its group ring, show: $K_i = \sum_{a_k\in cl_G(a_i)} a_k $, then $Z(\mathbb{C}[G])=span_\mathbb{C}(K_1,...,K_n)$

Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Checking Ideals of Rings

Find integer solutions of $xy=-1$ (using only elementary ring theory).

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