Question

Can a nilpotent element be an idempotent?

score 237 · Answer 1 · 2026-04-11 15:46:39

237

Views

Can a nilpotent element be an idempotent?

Published on 11 Apr 2026 - 15:46

score 181 · Answer 2 · 2026-04-15 12:46:16

181

Views

Do all (finite) group ring projections come from subgroups?

Published on 15 Apr 2026 - 12:46

score 127 · Answer 3 · 2026-05-11 08:39:42

127

Views

Prove that the $R$-module $I \bigoplus I$ is free on the generators $(2 ,1+\sqrt{-5})$ and $(1-\sqrt{-5},2)$.

Published on 11 May 2026 - 8:39

score 596 · Answer 4 · 2026-04-16 09:58:09

596

Views

If the intersection of all non-zero ideals of an integral domain R is non-zero, show that R is a field.

Published on 16 Apr 2026 - 9:58

score 138 · Answer 5 · 2026-04-16 23:54:04

138

Views

If an infinite ring has zero divisors, must it have infinitely many distinct zero divisors with the same annihilator?

Published on 16 Apr 2026 - 23:54

score 70 · Answer 6 · 2026-05-05 21:22:22

70

Views

Finding an integral subring of $k[x_1, ..., x_n]/P$ generated by $n$ algebraically independent elements

Published on 05 May 2026 - 21:22

score 171 · Answer 7 · 2026-04-16 14:21:44

171

Views

Faithful $S$-Noetherian module

Published on 16 Apr 2026 - 14:21

score 126 · Answer 8 · 2026-04-14 07:57:49

126

Views

Proving a corollary of the Chinese remainder theorem.

Published on 14 Apr 2026 - 7:57

score 66 · Answer 9 · 2026-04-13 08:59:55

66

Views

If $\mathfrak a_i/J(A)\cong\mathfrak a_j/J(A)$, then $\mathfrak a_i\cong\mathfrak a_j$

Published on 13 Apr 2026 - 8:59

score 100 · Answer 10 · 2026-05-05 22:17:43

100

Views

$R$ is ring with $a\subset R$ ideal. $M$ as $R-$module and submodule $N\subset M$. What is difference between $a$-adic topology and subspace topology?

Published on 05 May 2026 - 22:17

score 86 · Answer 11 · 2026-04-11 14:43:01

86

Views

Ring, ideal, homomorphism

Published on 11 Apr 2026 - 14:43

score 97 · Answer 12 · 2026-05-05 22:17:37

97

Views

Noetherian local ring with dualizing complex is quotient ring of a Gorenstein local ring?

Published on 05 May 2026 - 22:17

score 48 · Answer 13 · 2026-03-27 17:57:45

48

Views

If $V$ is a simple $R$-module and $R = S\oplus T$, then $V = SV \oplus TV$

Published on 27 Mar 2026 - 17:57

score 124 · Answer 14 · 2026-04-12 15:25:20

124

Views

greatest common divisor for polynomials

Published on 12 Apr 2026 - 15:25

score 73 · Answer 15 · 2026-04-16 00:29:23

73

Views

If $R$ is regular, is the quotient ring $R[x]/K[x]$ always Artinian or Noetherian?

Published on 16 Apr 2026 - 0:29

List Question

Can a nilpotent element be an idempotent?

Do all (finite) group ring projections come from subgroups?

Prove that the $R$-module $I \bigoplus I$ is free on the generators $(2 ,1+\sqrt{-5})$ and $(1-\sqrt{-5},2)$.

If the intersection of all non-zero ideals of an integral domain R is non-zero, show that R is a field.

If an infinite ring has zero divisors, must it have infinitely many distinct zero divisors with the same annihilator?

Finding an integral subring of $k[x_1, ..., x_n]/P$ generated by $n$ algebraically independent elements

Faithful $S$-Noetherian module

Proving a corollary of the Chinese remainder theorem.

If $\mathfrak a_i/J(A)\cong\mathfrak a_j/J(A)$, then $\mathfrak a_i\cong\mathfrak a_j$

$R$ is ring with $a\subset R$ ideal. $M$ as $R-$module and submodule $N\subset M$. What is difference between $a$-adic topology and subspace topology?

Ring, ideal, homomorphism

Noetherian local ring with dualizing complex is quotient ring of a Gorenstein local ring?

If $V$ is a simple $R$-module and $R = S\oplus T$, then $V = SV \oplus TV$

greatest common divisor for polynomials

If $R$ is regular, is the quotient ring $R[x]/K[x]$ always Artinian or Noetherian?

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