Question

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

score 110 · Answer 1 · 2026-04-16 01:27:07

110

Views

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

Published on 16 Apr 2026 - 1:27

score 144 · Answer 2 · 2026-04-13 19:50:44

144

Views

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

Published on 13 Apr 2026 - 19:50

score 185 · Answer 3 · 2026-04-12 18:00:11

185

Views

Isomorphisms between finite fields

Published on 12 Apr 2026 - 18:00

score 131 · Answer 4 · 2026-04-16 12:06:00

131

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 16 Apr 2026 - 12:06

score 52 · Answer 5 · 2026-04-17 13:28:48

52

Views

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

Published on 17 Apr 2026 - 13:28

score 55 · Answer 6 · 2026-04-13 15:10:54

55

Views

Isomorphism between C and another ring

Published on 13 Apr 2026 - 15:10

score 140 · Answer 7 · 2026-04-15 00:23:30

140

Views

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

Published on 15 Apr 2026 - 0:23

score 562 · Answer 8 · 2026-04-16 01:39:17

562

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 16 Apr 2026 - 1:39

score 1.5k · Answer 9 · 2026-05-10 15:47:13

1.5k

Views

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

Published on 10 May 2026 - 15:47

score 127 · Answer 10 · 2026-04-10 19:26:12

127

Views

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

Published on 10 Apr 2026 - 19:26

score 50 · Answer 11 · 2026-05-10 16:10:00

50

Views

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

Published on 10 May 2026 - 16:10

score 170 · Answer 12 · 2026-04-12 16:10:03

170

Views

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

Published on 12 Apr 2026 - 16:10

score 141 · Answer 13 · 2026-04-17 07:29:12

141

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 17 Apr 2026 - 7:29

score 556 · Answer 14 · 2026-04-09 10:15:06

556

Views

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

Published on 09 Apr 2026 - 10:15

score 328 · Answer 15 · 2026-04-16 23:07:16

328

Views

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

Published on 16 Apr 2026 - 23:07

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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