Question

If $p(X),q(X)\in R[X]$ are primitive and $R$ is an integral domain, then $ap(X)=bq(X)$ imply $a$ and $b$ are associates.

score 37 · Answer 1 · 2019-07-12 04:07:05

37

Views

If $p(X),q(X)\in R[X]$ are primitive and $R$ is an integral domain, then $ap(X)=bq(X)$ imply $a$ and $b$ are associates.

Published on 12 Jul 2019 - 4:07

score 647 · Answer 2 · 2026-03-27 07:50:22

647

Views

Prove that $f:R\to S^{-1}R$ is injective iff $S$ is a subset of the set all elements which are not zero-divisors of $R$

Published on 27 Mar 2026 - 7:50

score 47 · Answer 3 · 2019-07-12 20:21:22

47

Views

Find $a\in \mathbb{Z}_5[x] /I$ so $a^3=x^2+1+I$

Published on 12 Jul 2019 - 20:21

score 35 · Answer 4 · 2019-07-13 15:17:59

35

Views

Defining an isomorphism from $\mathbb{R}[x]/(f(x))$ to $\mathbb{C}$

Published on 13 Jul 2019 - 15:17

score 108 · Answer 5 · 2026-04-08 20:09:02

108

Views

Some question of ideal

Published on 08 Apr 2026 - 20:09

score 290 · Answer 6 · 2026-03-25 10:57:15

290

Views

Prove no zero divisors of a ring with a radical in $\mathbb{Z}_7$

Published on 25 Mar 2026 - 10:57

score 219 · Answer 7 · 2026-03-25 10:58:54

219

Views

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

Published on 25 Mar 2026 - 10:58

score 250 · Answer 8 · 2019-07-13 21:26:18

250

Views

Property of Henselian Rings in Milne's Etale Cohomology

Published on 13 Jul 2019 - 21:26

score 101 · Answer 9 · 2019-07-13 21:34:31

101

Views

Is there an injective ring homomorphism from $\Bbb R \oplus \Bbb R$ to $C(\Bbb R)$?

Published on 13 Jul 2019 - 21:34

score 431 · Answer 10 · 2026-03-25 10:56:00

431

Views

The only idempotent element in $\Bbb Z_{51}$ are $0$ and $1$.

Published on 25 Mar 2026 - 10:56

score 338 · Answer 11 · 2019-07-14 01:22:18

338

Views

$k$-Module direct sum of Finite Separable Extension Fields iff Kahler Differentials vanish

Published on 14 Jul 2019 - 1:22

score 156 · Answer 12 · 2026-03-25 11:08:47

156

Views

Non-zero Jacobi Determinant implies Flatness

Published on 25 Mar 2026 - 11:08

score 88 · Answer 13 · 2026-03-31 17:29:34

88

Views

Find the number of the ideals in this ring.

Published on 31 Mar 2026 - 17:29

score 1.5k · Answer 14 · 2019-07-14 11:28:38

1.5k

Views

Describe the maximal ideals in the ring of Gaussian Integers $\Bbb Z[i]$.

Published on 14 Jul 2019 - 11:28

score 235 · Answer 15 · 2026-03-31 17:26:26

235

Views

$\mathbb{C}$ as a quotient of $\mathbb{R}[x]$ by the principal ideal of $x^2 + 1$

Published on 31 Mar 2026 - 17:26

List Question

If $p(X),q(X)\in R[X]$ are primitive and $R$ is an integral domain, then $ap(X)=bq(X)$ imply $a$ and $b$ are associates.

Prove that $f:R\to S^{-1}R$ is injective iff $S$ is a subset of the set all elements which are not zero-divisors of $R$

Find $a\in \mathbb{Z}_5[x] /I$ so $a^3=x^2+1+I$

Defining an isomorphism from $\mathbb{R}[x]/(f(x))$ to $\mathbb{C}$

Some question of ideal

Prove no zero divisors of a ring with a radical in $\mathbb{Z}_7$

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

Property of Henselian Rings in Milne's Etale Cohomology

Is there an injective ring homomorphism from $\Bbb R \oplus \Bbb R$ to $C(\Bbb R)$?

The only idempotent element in $\Bbb Z_{51}$ are $0$ and $1$.

$k$-Module direct sum of Finite Separable Extension Fields iff Kahler Differentials vanish

Non-zero Jacobi Determinant implies Flatness

Find the number of the ideals in this ring.

Describe the maximal ideals in the ring of Gaussian Integers $\Bbb Z[i]$.

$\mathbb{C}$ as a quotient of $\mathbb{R}[x]$ by the principal ideal of $x^2 + 1$

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