Question

Help proving an alternative version of Chinese Residue Theorem in the ring of polynomials.

score 76 · Answer 1 · 2026-03-31 22:51:10

76

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Help proving an alternative version of Chinese Residue Theorem in the ring of polynomials.

Published on 31 Mar 2026 - 22:51

score 36 · Answer 2 · 2019-04-05 21:58:52

36

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Basic Assumptions about Ring Operations

Published on 05 Apr 2019 - 21:58

score 47 · Answer 3 · 2026-03-30 20:43:01

47

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Let $I = n\mathbb{Z}$ , $J = m\mathbb{Z}$. Does $I+J = I \cap J = IJ = I/J = d\mathbb{Z}$???

Published on 30 Mar 2026 - 20:43

score 223 · Answer 4 · 2026-03-30 20:41:05

223

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Ideal generator of a quotient ring

Published on 30 Mar 2026 - 20:41

score 29 · Answer 5 · 2026-04-02 02:09:18

29

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What is interpretation of follwing lemma?

Published on 02 Apr 2026 - 2:09

score 261 · Answer 6 · 2026-03-26 22:19:46

261

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Units, Prime Elements and Irreducible elements for polynomials

Published on 26 Mar 2026 - 22:19

score 157 · Answer 7 · 2026-04-01 02:31:06

157

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Visualizing euclidean rings

Published on 01 Apr 2026 - 2:31

score 1.7k · Answer 8 · 2019-04-06 13:24:00

1.7k

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Is Ring $\mathbb C[x]/(x^2+1) \cong \mathbb C$

Published on 06 Apr 2019 - 13:24

score 189 · Answer 9 · 2026-03-30 22:51:38

189

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Prove : If $I=(p(x))$ is a prime ideal in $ F[x]$ then $p(x)$ is irreducible.my claim is F need not to be field.

Published on 30 Mar 2026 - 22:51

score 210 · Answer 10 · 2026-03-25 04:41:35

210

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In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

Published on 25 Mar 2026 - 4:41

score 398 · Answer 11 · 2026-03-25 23:51:43

398

Views

Every short exact sequence with a simple module splits

Published on 25 Mar 2026 - 23:51

score 187 · Answer 12 · 2026-04-01 00:28:37

187

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Let k⊆K⊆E fields and if E/k is a finite extension, the E/K and K/k are also finite extensions.

Published on 01 Apr 2026 - 0:28

score 86 · Answer 13 · 2026-04-01 00:28:37

86

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$K$ cannot have subfields $k'$ and $k''$ such $k' \cong \mathbb{Q}$ and $k'' \cong \mathbb{F}_{p}$ where $p$ is some prime.

Published on 01 Apr 2026 - 0:28

score 78 · Answer 14 · 2026-04-02 02:12:28

78

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Prove that the map $f: \Bbb C \times \Bbb C \to \Bbb C \times \Bbb C$ by $f(z_1,z_2)=(z_1z_2,z_1\bar{z_2})$ is an $\Bbb R $ bilinear map

Published on 02 Apr 2026 - 2:12

score 1.1k · Answer 15 · 2019-04-08 02:49:32

1.1k

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How to show $\mathbb Z_2[x]/(x^3+x+1)$ is isomorphic to $\mathbb Z_2[x]/(x^3+x^2+1)$

Published on 08 Apr 2019 - 2:49

List Question

Help proving an alternative version of Chinese Residue Theorem in the ring of polynomials.

Basic Assumptions about Ring Operations

Let $I = n\mathbb{Z}$ , $J = m\mathbb{Z}$. Does $I+J = I \cap J = IJ = I/J = d\mathbb{Z}$???

Ideal generator of a quotient ring

What is interpretation of follwing lemma?

Units, Prime Elements and Irreducible elements for polynomials

Visualizing euclidean rings

Is Ring $\mathbb C[x]/(x^2+1) \cong \mathbb C$

Prove : If $I=(p(x))$ is a prime ideal in $ F[x]$ then $p(x)$ is irreducible.my claim is F need not to be field.

In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

Every short exact sequence with a simple module splits

Let k⊆K⊆E fields and if E/k is a finite extension, the E/K and K/k are also finite extensions.

$K$ cannot have subfields $k'$ and $k''$ such $k' \cong \mathbb{Q}$ and $k'' \cong \mathbb{F}_{p}$ where $p$ is some prime.

Prove that the map $f: \Bbb C \times \Bbb C \to \Bbb C \times \Bbb C$ by $f(z_1,z_2)=(z_1z_2,z_1\bar{z_2})$ is an $\Bbb R $ bilinear map

How to show $\mathbb Z_2[x]/(x^3+x+1)$ is isomorphic to $\mathbb Z_2[x]/(x^3+x^2+1)$

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