Question

Finding monic generator for ideals generated by polynomials of $\mathbb{Q}[X]$

score 182 · Answer 1 · 2026-03-31 11:52:29

182

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Finding monic generator for ideals generated by polynomials of $\mathbb{Q}[X]$

Published on 31 Mar 2026 - 11:52

score 167 · Answer 2 · 2026-03-25 17:17:20

167

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Why called double centralizer property?

Published on 25 Mar 2026 - 17:17

score 321 · Answer 3 · 2026-03-29 11:49:56

321

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Easy counterexamples for each containment $Field\subsetneq ED \subsetneq PID \subsetneq UFD \subsetneq GCD \subsetneq Integral\space Domain$

Published on 29 Mar 2026 - 11:49

score 62 · Answer 4 · 2019-06-04 12:31:40

62

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Concerning $(x,y) \mapsto (\lambda x^2y+A,\mu x^{-1}+B)$

Published on 04 Jun 2019 - 12:31

score 141 · Answer 5 · 2026-03-25 07:45:40

141

Views

Is the fiber product of local artinian rings again local artinian under these conditions?

Published on 25 Mar 2026 - 7:45

score 53 · Answer 6 · 2019-06-05 16:34:30

53

Views

Prove that given two elements $a,b$ of relatively prime degree in a field extension $K$, $F(a) \cap F(b) = F$

Published on 05 Jun 2019 - 16:34

score 125 · Answer 7 · 2026-03-26 02:55:02

125

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$\mathbb Z[x]/(x^2-2,5) \cong \mathbb Z/5\mathbb Z[x]/(x^2-2)$

Published on 26 Mar 2026 - 2:55

score 49 · Answer 8 · 2026-03-27 18:34:42

49

Views

Simplify the ideal $(5+23i, 341)$ in $\mathbb Z[i]$

Published on 27 Mar 2026 - 18:34

score 69 · Answer 9 · 2026-04-03 17:55:31

69

Views

What is polynomial $p = (X-X_{1})(X-X_{2}) \cdots (X-X_{m})$ in $R[X_{1}, \ldots, X_{m}][X]$?

Published on 03 Apr 2026 - 17:55

score 519 · Answer 10 · 2026-04-02 19:48:14

519

Views

Radical of Annihilator identity

Published on 02 Apr 2026 - 19:48

score 148 · Answer 11 · 2019-06-06 12:10:15

148

Views

Image of a linear transformation with a matrix in $\mathbb Z_m$

Published on 06 Jun 2019 - 12:10

score 53 · Answer 12 · 2026-03-27 02:07:09

53

Views

The polynomial $X-2Y$ in $\Bbb Z_{13}[X,Y]$ is irredicible

Published on 27 Mar 2026 - 2:07

score 44 · Answer 13 · 2026-04-07 14:43:35

44

Views

For each $\sigma \in \mathrm{S}_{m}$, $p \mapsto \sigma \cdot p$ is an automorphism of $R[X_{1}, \ldots, X_{m}]$

Published on 07 Apr 2026 - 14:43

score 101 · Answer 14 · 2026-03-31 09:28:56

101

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Find an ideal $I$ of $\mathbb Z/2\mathbb Z[x]$, such that $\mathbb Z/2\mathbb Z[x]/I$ is a field of 8 elements.

Published on 31 Mar 2026 - 9:28

score 955 · Answer 15 · 2026-03-30 10:36:40

955

Views

Why does the universal enveloping algebra not have zero-divisors?

Published on 30 Mar 2026 - 10:36

List Question

Finding monic generator for ideals generated by polynomials of $\mathbb{Q}[X]$

Why called double centralizer property?

Easy counterexamples for each containment $Field\subsetneq ED \subsetneq PID \subsetneq UFD \subsetneq GCD \subsetneq Integral\space Domain$

Concerning $(x,y) \mapsto (\lambda x^2y+A,\mu x^{-1}+B)$

Is the fiber product of local artinian rings again local artinian under these conditions?

Prove that given two elements $a,b$ of relatively prime degree in a field extension $K$, $F(a) \cap F(b) = F$

$\mathbb Z[x]/(x^2-2,5) \cong \mathbb Z/5\mathbb Z[x]/(x^2-2)$

Simplify the ideal $(5+23i, 341)$ in $\mathbb Z[i]$

What is polynomial $p = (X-X_{1})(X-X_{2}) \cdots (X-X_{m})$ in $R[X_{1}, \ldots, X_{m}][X]$?

Radical of Annihilator identity

Image of a linear transformation with a matrix in $\mathbb Z_m$

The polynomial $X-2Y$ in $\Bbb Z_{13}[X,Y]$ is irredicible

For each $\sigma \in \mathrm{S}_{m}$, $p \mapsto \sigma \cdot p$ is an automorphism of $R[X_{1}, \ldots, X_{m}]$

Find an ideal $I$ of $\mathbb Z/2\mathbb Z[x]$, such that $\mathbb Z/2\mathbb Z[x]/I$ is a field of 8 elements.

Why does the universal enveloping algebra not have zero-divisors?

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