Question

Product of ideals for Nakayama's Lemma

score 168 · Answer 1 · 2026-04-30 08:07:46

168

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Product of ideals for Nakayama's Lemma

Published on 30 Apr 2026 - 8:07

score 83 · Answer 2 · 2026-04-18 16:26:00

83

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What are the $2$-dimensional algebras over any arbitrary field?

Published on 18 Apr 2026 - 16:26

score 114 · Answer 3 · 2026-04-16 08:39:25

114

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Prove that in a ring with at least two elements $0\neq 1$.

Published on 16 Apr 2026 - 8:39

score 660 · Answer 4 · 2026-04-15 01:13:37

660

Views

If a polynomial ring has a zero divisor, then the ring has a zero divisor

Published on 15 Apr 2026 - 1:13

score 358 · Answer 5 · 2026-04-12 08:22:24

358

Views

Describing the ring $\mathbb{Z}[x]/(x-8,2x-6)$

Published on 12 Apr 2026 - 8:22

score 294 · Answer 6 · 2026-04-14 12:50:49

294

Views

Does a ring map $f:R\to S$ induce a homomorphism $GL_n(R)\to GL_n(S)$?

Published on 14 Apr 2026 - 12:50

score 39 · Answer 7 · 2026-04-16 17:42:38

39

Views

Why $f(0)\neq 0$ where $f $ is a polynomial over the field $\mathbb F_q$ and $\deg(f)=m > 0$?

Published on 16 Apr 2026 - 17:42

score 219 · Answer 8 · 2026-04-14 01:43:56

219

Views

When does a ring map $R\to S$ produce a group epimorphism $GL_n(R)\to GL_n(S)$?

Published on 14 Apr 2026 - 1:43

score 34 · Answer 9 · 2026-04-12 00:50:58

34

Views

When is $r = r^{2}$ in $\mathbb{Z}/p^{l}\mathbb{Z}$?

Published on 12 Apr 2026 - 0:50

score 177 · Answer 10 · 2026-04-16 13:53:02

177

Views

On Bounded Index of Nilpotency of $R[x]$ and $M_n(R)$

Published on 16 Apr 2026 - 13:53

score 76 · Answer 11 · 2026-04-28 11:00:38

76

Views

Given $x$ and $y$ in $\mathbb{Z}[i]$, find $q$ and $r$ such that $x=qy+r$.

Published on 28 Apr 2026 - 11:00

score 111 · Answer 12 · 2026-04-13 21:32:56

111

Views

Prove that $I$ is a maximal ideal

Published on 13 Apr 2026 - 21:32

score 85 · Answer 13 · 2026-04-14 20:52:52

85

Views

Show that a polynomial f(x) over a field k is irreducible if and only if the polynomial f(x + 1) is irreducible.

Published on 14 Apr 2026 - 20:52

score 354 · Answer 14 · 2026-04-18 21:16:22

354

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Find a non-principal ideal (if there exists any) in the rings Z[x], Q[x], Q[x, y]

Published on 18 Apr 2026 - 21:16

score 257 · Answer 15 · 2026-04-14 11:54:15

257

Views

Proof of Gauss lemma

Published on 14 Apr 2026 - 11:54

List Question

Product of ideals for Nakayama's Lemma

What are the $2$-dimensional algebras over any arbitrary field?

Prove that in a ring with at least two elements $0\neq 1$.

If a polynomial ring has a zero divisor, then the ring has a zero divisor

Describing the ring $\mathbb{Z}[x]/(x-8,2x-6)$

Does a ring map $f:R\to S$ induce a homomorphism $GL_n(R)\to GL_n(S)$?

Why $f(0)\neq 0$ where $f $ is a polynomial over the field $\mathbb F_q$ and $\deg(f)=m > 0$?

When does a ring map $R\to S$ produce a group epimorphism $GL_n(R)\to GL_n(S)$?

When is $r = r^{2}$ in $\mathbb{Z}/p^{l}\mathbb{Z}$?

On Bounded Index of Nilpotency of $R[x]$ and $M_n(R)$

Given $x$ and $y$ in $\mathbb{Z}[i]$, find $q$ and $r$ such that $x=qy+r$.

Prove that $I$ is a maximal ideal

Show that a polynomial f(x) over a field k is irreducible if and only if the polynomial f(x + 1) is irreducible.

Find a non-principal ideal (if there exists any) in the rings Z[x], Q[x], Q[x, y]

Proof of Gauss lemma

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