Question

Concerning $Frac((Frac \space D)[x])$ and $Frac(D[x])$ for an integral domain $D$

score 76 · Answer 1 · 2015-04-06 15:51:09

76

Views

Concerning $Frac((Frac \space D)[x])$ and $Frac(D[x])$ for an integral domain $D$

Published on 06 Apr 2015 - 15:51

score 428 · Answer 2 · 2015-04-06 23:50:41

428

Views

An integral domain with Krull dimension 1 which is neither Noetherian nor integrally closed

Published on 06 Apr 2015 - 23:50

score 2.9k · Answer 3 · 2015-04-11 13:02:10

2.9k

Views

Looking for an example of a GCD domain which is not a UFD

Published on 11 Apr 2015 - 13:02

score 695 · Answer 4 · 2015-04-11 13:42:30

695

Views

How to show that $\mathbb Z+x \mathbb Q[x]$ is a GCD domain?

Published on 11 Apr 2015 - 13:42

score 975 · Answer 5 · 2015-04-11 18:28:51

975

Views

Integral Domains and Unique Factorisation Domains

Published on 11 Apr 2015 - 18:28

score 896 · Answer 6 · 2015-04-14 08:37:03

896

Views

Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?

Published on 14 Apr 2015 - 8:37

score 206 · Answer 7 · 2015-04-16 12:38:18

206

Views

On non-constant multiplicative norms on integral domain and when does the absolute value of the norm is unity implies the element is unit?

Published on 16 Apr 2015 - 12:38

score 1.4k · Answer 8 · 2015-04-24 11:08:43

1.4k

Views

Prove that if $R$ is an integral domain and has ACCP, then $R[X]$ has ACCP

Published on 24 Apr 2015 - 11:08

score 116 · Answer 9 · 2015-04-26 18:17:09

116

Views

Integral domains examples

Published on 26 Apr 2015 - 18:17

score 427 · Answer 10 · 2015-04-27 00:13:22

427

Views

If $P$ is a prime then $R/P$ is an integral domain.

Published on 27 Apr 2015 - 0:13

score 411 · Answer 11 · 2015-04-27 21:18:10

411

Views

Show that $S$ is a field

Published on 27 Apr 2015 - 21:18

score 100 · Answer 12 · 2015-05-01 23:04:28

100

Views

Rings isomorphic to $\mathbb{Z}_6\times\mathbb{Z}_{10}$

Published on 01 May 2015 - 23:04

score 32 · Answer 13 · 2015-05-03 16:25:32

32

Views

$R$ has no zero divisors . Let $a \in R$ , $0 \ne b \in R$ and $0 \ne n \in \mathbb Z$ be such that $na+ab=0$ , then is it true that $a=0$?

Published on 03 May 2015 - 16:25

score 765 · Answer 14 · 2015-05-03 16:26:53

765

Views

Prove $R$ conatins an ideal that is not finitely generated. $R = F[x,x^2 y,\ldots,x^n y^{n-1},\ldots]$

Published on 03 May 2015 - 16:26

score 1k · Answer 15 · 2015-05-05 04:07:41

1k

Views

Prove or disprove $R= \mathbb Q[x]/\langle x^3-x^2+x-1 \rangle$ is an integral domain.

Published on 05 May 2015 - 4:07

List Question

Concerning $Frac((Frac \space D)[x])$ and $Frac(D[x])$ for an integral domain $D$

An integral domain with Krull dimension 1 which is neither Noetherian nor integrally closed

Looking for an example of a GCD domain which is not a UFD

How to show that $\mathbb Z+x \mathbb Q[x]$ is a GCD domain?

Integral Domains and Unique Factorisation Domains

Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?

On non-constant multiplicative norms on integral domain and when does the absolute value of the norm is unity implies the element is unit?

Prove that if $R$ is an integral domain and has ACCP, then $R[X]$ has ACCP

Integral domains examples

If $P$ is a prime then $R/P$ is an integral domain.

Show that $S$ is a field

Rings isomorphic to $\mathbb{Z}_6\times\mathbb{Z}_{10}$

$R$ has no zero divisors . Let $a \in R$ , $0 \ne b \in R$ and $0 \ne n \in \mathbb Z$ be such that $na+ab=0$ , then is it true that $a=0$?

Prove $R$ conatins an ideal that is not finitely generated. $R = F[x,x^2 y,\ldots,x^n y^{n-1},\ldots]$

Prove or disprove $R= \mathbb Q[x]/\langle x^3-x^2+x-1 \rangle$ is an integral domain.

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