Question

Finding all polynomials $p(x)$ such that $ \mathbb{Q}[x]/p(x) \simeq \mathbb{Q}(A)$ for fixed $A$ algebraic

score 109 · Answer 1 · 2026-03-25 22:25:09

109

Views

Finding all polynomials $p(x)$ such that $ \mathbb{Q}[x]/p(x) \simeq \mathbb{Q}(A)$ for fixed $A$ algebraic

Published on 25 Mar 2026 - 22:25

score 142 · Answer 2 · 2019-04-28 21:18:11

142

Views

How to prove ring isomorphism ${\mathbb{C}[x]}/{(x^2 + 2x)} \cong \mathbb{C} \oplus \mathbb{C}$

Published on 28 Apr 2019 - 21:18

score 181 · Answer 3 · 2019-04-30 11:58:33

181

Views

Isomorphisms between finite fields

Published on 30 Apr 2019 - 11:58

score 128 · Answer 4 · 2019-05-15 16:11:40

128

Views

Prove: If $\mathit R$ is a commutative ring with unity and $\mathit I=(x)\subseteq R[x]$, then $R[x] / (x)\cong R$

Published on 15 May 2019 - 16:11

score 49 · Answer 5 · 2019-05-18 03:22:50

49

Views

Let $K$ be a ring. Then $K[X_1,X_2] \cong K[X_1][X_2]$

Published on 18 May 2019 - 3:22

score 52 · Answer 6 · 2019-05-18 18:44:42

52

Views

Isomorphism between C and another ring

Published on 18 May 2019 - 18:44

score 137 · Answer 7 · 2019-05-23 02:23:36

137

Views

When can we "reduce" $(n\Bbb Z/m\Bbb Z)$?

Published on 23 May 2019 - 2:23

score 559 · Answer 8 · 2019-05-27 02:42:10

559

Views

Let $I$ be an ideal of a ring $(R,+,\cdot)$. Prove that the quotient homomorphism $\varphi : R \rightarrow R / I$ is a ring homomorphism

Published on 27 May 2019 - 2:42

score 1.5k · Answer 9 · 2026-03-25 04:41:33

1.5k

Views

Every Artinian ring is isomorphic to a direct product of Artinian local rings

Published on 25 Mar 2026 - 4:41

score 124 · Answer 10 · 2019-06-06 04:59:20

124

Views

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

Published on 06 Jun 2019 - 4:59

score 45 · Answer 11 · 2026-03-25 13:42:12

45

Views

$End_{R}(R)\cong R$

Published on 25 Mar 2026 - 13:42

score 167 · Answer 12 · 2019-06-13 06:36:50

167

Views

General intuition behind Ring isomorphism when it involves Polynomial Rings and help for proving it.

Published on 13 Jun 2019 - 6:36

score 138 · Answer 13 · 2019-06-18 01:35:48

138

Views

Let $R$ be a commutative ring and $a_1, \dots, a_n$ elements of $R$. Prove that $\frac{R[x_1, \dots, x_n]}{(x_1-a_1, \dots, x_n-a_n)} \cong R.$

Published on 18 Jun 2019 - 1:35

score 555 · Answer 14 · 2026-02-23 06:09:11

555

Views

If $R$ and $S$ are isomorphic rings, is $R$ an ordered ring iff $S$ is an ordered ring?

Published on 23 Feb 2026 - 6:09

score 325 · Answer 15 · 2019-09-11 00:01:45

325

Views

Are the fields $\mathbb{Q}$ and $\mathbb{Q[\sqrt2]}$ isomorphic?

Published on 11 Sep 2019 - 0:01

List Question

Finding all polynomials $p(x)$ such that $ \mathbb{Q}[x]/p(x) \simeq \mathbb{Q}(A)$ for fixed $A$ algebraic

How to prove ring isomorphism ${\mathbb{C}[x]}/{(x^2 + 2x)} \cong \mathbb{C} \oplus \mathbb{C}$

Isomorphisms between finite fields

Prove: If $\mathit R$ is a commutative ring with unity and $\mathit I=(x)\subseteq R[x]$, then $R[x] / (x)\cong R$

Let $K$ be a ring. Then $K[X_1,X_2] \cong K[X_1][X_2]$

Isomorphism between C and another ring

When can we "reduce" $(n\Bbb Z/m\Bbb Z)$?

Let $I$ be an ideal of a ring $(R,+,\cdot)$. Prove that the quotient homomorphism $\varphi : R \rightarrow R / I$ is a ring homomorphism

Every Artinian ring is isomorphic to a direct product of Artinian local rings

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

$End_{R}(R)\cong R$

General intuition behind Ring isomorphism when it involves Polynomial Rings and help for proving it.

Let $R$ be a commutative ring and $a_1, \dots, a_n$ elements of $R$. Prove that $\frac{R[x_1, \dots, x_n]}{(x_1-a_1, \dots, x_n-a_n)} \cong R.$

If $R$ and $S$ are isomorphic rings, is $R$ an ordered ring iff $S$ is an ordered ring?

Are the fields $\mathbb{Q}$ and $\mathbb{Q[\sqrt2]}$ isomorphic?

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