Question

Pick out the integral domains from the following list of rings

score 267 · Answer 1 · 2026-03-28 00:05:32

267

Views

Pick out the integral domains from the following list of rings

Published on 28 Mar 2026 - 0:05

score 133 · Answer 2 · 2026-03-26 17:36:52

133

Views

A false proof for the theorem about finite integral domains and fields

Published on 26 Mar 2026 - 17:36

score 179 · Answer 3 · 2017-09-04 13:04:30

179

Views

$K \otimes_R A$ is Noetherian ring where $R$ is integral domain with field of fractions $K$ and $A$ an $R$-algebra which is Noetherian ring

Published on 04 Sep 2017 - 13:04

score 498 · Answer 4 · 2017-09-15 11:38:51

498

Views

Prove that $\mathbb{Z}[\omega]$ is an integral domain

Published on 15 Sep 2017 - 11:38

score 103 · Answer 5 · 2026-03-27 13:20:08

103

Views

Modules and homomorphism on a domain

Published on 27 Mar 2026 - 13:20

score 9.7k · Answer 6 · 2017-10-01 20:54:17

9.7k

Views

$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$

Published on 01 Oct 2017 - 20:54

score 535 · Answer 7 · 2026-02-23 04:02:31

535

Views

Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Published on 23 Feb 2026 - 4:02

score 83 · Answer 8 · 2017-10-17 09:57:54

83

Views

Is the quotient ring $\Bbb{Z}_7[x]/\langle 3x^3 + 4x^2 + 6x + 4\rangle$ an integral domain?

Published on 17 Oct 2017 - 9:57

score 182 · Answer 9 · 2017-10-20 10:39:34

182

Views

Prove that there are infinitely many values of $α$ for which $f(x)= x^{7} +15x^{2} − 30x + α$ is irreducible in Q[x]

Published on 20 Oct 2017 - 10:39

score 1.5k · Answer 10 · 2017-10-31 20:07:40

1.5k

Views

Cancellation law in a ring without unity

Published on 31 Oct 2017 - 20:07

score 179 · Answer 11 · 2017-11-13 21:23:53

179

Views

If $A$ is an integral domain and $a^2=1$, then $a=1$ or $a=-1$

Published on 13 Nov 2017 - 21:23

score 700 · Answer 12 · 2017-11-15 01:19:03

700

Views

Show that $\mathbb{C} \otimes_\mathbb{R} \mathbb{C}$ is not an integral domain

Published on 15 Nov 2017 - 1:19

score 92 · Answer 13 · 2017-11-16 14:57:02

92

Views

Calculate: $\iint_D{dxdy} \text{ from the region: } D = \{(x,y) \in R^2 : 0 \le y \le \frac{3}{4}x,\ x^2+y^2\le25 \}$

Published on 16 Nov 2017 - 14:57

score 89 · Answer 14 · 2017-11-26 12:56:51

89

Views

$\phi: A\to A_S$ is an embedding for every multiplicatively closed set S $\implies$ A is integral

Published on 26 Nov 2017 - 12:56

score 126 · Answer 15 · 2017-12-06 22:42:46

126

Views

Common factors of $f, \lambda g$ when $\lambda \in R$, $f,g \in R[x]$ have only constant common factors.

Published on 06 Dec 2017 - 22:42

List Question

Pick out the integral domains from the following list of rings

A false proof for the theorem about finite integral domains and fields

$K \otimes_R A$ is Noetherian ring where $R$ is integral domain with field of fractions $K$ and $A$ an $R$-algebra which is Noetherian ring

Prove that $\mathbb{Z}[\omega]$ is an integral domain

Modules and homomorphism on a domain

$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$

Prove that the ideal $I = \left( 3, 2 + \sqrt{-5} \right)$ is a prime ideal in $\mathbb{Z}\left[ \sqrt{-5} \right]$.

Is the quotient ring $\Bbb{Z}_7[x]/\langle 3x^3 + 4x^2 + 6x + 4\rangle$ an integral domain?

Prove that there are infinitely many values of $α$ for which $f(x)= x^{7} +15x^{2} − 30x + α$ is irreducible in Q[x]

Cancellation law in a ring without unity

If $A$ is an integral domain and $a^2=1$, then $a=1$ or $a=-1$

Show that $\mathbb{C} \otimes_\mathbb{R} \mathbb{C}$ is not an integral domain

Calculate: $\iint_D{dxdy} \text{ from the region: } D = \{(x,y) \in R^2 : 0 \le y \le \frac{3}{4}x,\ x^2+y^2\le25 \}$

$\phi: A\to A_S$ is an embedding for every multiplicatively closed set S $\implies$ A is integral

Common factors of $f, \lambda g$ when $\lambda \in R$, $f,g \in R[x]$ have only constant common factors.

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