Question

A fraction field is not finitely generated over its subdomain

score 2.6k · Answer 1 · 2013-02-23 05:55:13

2.6k

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A fraction field is not finitely generated over its subdomain

Published on 23 Feb 2013 - 5:55

score 127 · Answer 2 · 2020-08-05 10:48:32

127

Views

Is $\mathbb Q \times \{0\}$ an integral domain?

Published on 05 Aug 2020 - 10:48

score 36 · Answer 3 · 2020-08-11 09:48:50

36

Views

How to show $u \in R^{x} \implies u \in R[X]^{x}$ for integral domain $(R,+, \times)$

Published on 11 Aug 2020 - 9:48

score 128 · Answer 4 · 2020-08-14 00:45:25

128

Views

Find all primes such that $x^{2} = -1$ has no solution in $\mathbb{F}_p$

Published on 14 Aug 2020 - 0:45

score 47 · Answer 5 · 2020-08-16 01:23:41

47

Views

If $K^{\times}/R^{\times}$ is a free abelian group, then must $R$ be a UFD?

Published on 16 Aug 2020 - 1:23

score 153 · Answer 6 · 2026-02-23 15:27:43

153

Views

Certain separable ring extensions

Published on 23 Feb 2026 - 15:27

score 722 · Answer 7 · 2020-09-03 06:54:09

722

Views

What is principal ideal generated by $p$?

Published on 03 Sep 2020 - 6:54

score 46 · Answer 8 · 2020-09-11 15:36:17

46

Views

If $N\otimes_A B$ and $N\otimes_A B'$ are projective modules, what about $N$?

Published on 11 Sep 2020 - 15:36

score 228 · Answer 9 · 2020-09-11 19:45:16

228

Views

How to check if some ring is an integral domain?

Published on 11 Sep 2020 - 19:45

score 206 · Answer 10 · 2020-09-25 04:23:00

206

Views

Is $f:A\to B$ is an injective finite type homomorphism of integral domains, then $\text{Frac}(B)$ is finite dimensional over $\text{Frac}(A)$.

Published on 25 Sep 2020 - 4:23

score 798 · Answer 11 · 2020-09-27 23:59:36

798

Views

Show that the integral closure of $\mathbb{Z}[\sqrt{5}]$ in $\text{Quot}\mathbb{Z}[\sqrt{5}]$ is $\mathbb{Z}[\frac{1+\sqrt{5}}{2}]$

Published on 27 Sep 2020 - 23:59

score 126 · Answer 12 · 2020-10-01 16:30:18

126

Views

$a+b\sqrt{5}$ is prime in $\mathbb{Z}[\sqrt{5}]$ if its norm $N(a+b\sqrt{5})=a^2-5b^2$ is prime in $\mathbb{Z}$

Published on 01 Oct 2020 - 16:30

score 60 · Answer 13 · 2020-10-01 19:31:18

60

Views

Definition and evaluation of polynomial functions

Published on 01 Oct 2020 - 19:31

score 27 · Answer 14 · 2020-10-14 09:50:14

27

Views

finding the elements of equivalence class that contains $(-5,8)$ on the relation $\sim$ in $D\times S$ as follows

Published on 14 Oct 2020 - 9:50

score 67 · Answer 15 · 2020-10-18 20:15:59

67

Views

What is the reason to stipulate $0 \neq 1$ in the definition of Ordered Integral Domains?

Published on 18 Oct 2020 - 20:15

List Question

A fraction field is not finitely generated over its subdomain

Is $\mathbb Q \times \{0\}$ an integral domain?

How to show $u \in R^{x} \implies u \in R[X]^{x}$ for integral domain $(R,+, \times)$

Find all primes such that $x^{2} = -1$ has no solution in $\mathbb{F}_p$

If $K^{\times}/R^{\times}$ is a free abelian group, then must $R$ be a UFD?

Certain separable ring extensions

What is principal ideal generated by $p$?

If $N\otimes_A B$ and $N\otimes_A B'$ are projective modules, what about $N$?

How to check if some ring is an integral domain?

Is $f:A\to B$ is an injective finite type homomorphism of integral domains, then $\text{Frac}(B)$ is finite dimensional over $\text{Frac}(A)$.

Show that the integral closure of $\mathbb{Z}[\sqrt{5}]$ in $\text{Quot}\mathbb{Z}[\sqrt{5}]$ is $\mathbb{Z}[\frac{1+\sqrt{5}}{2}]$

$a+b\sqrt{5}$ is prime in $\mathbb{Z}[\sqrt{5}]$ if its norm $N(a+b\sqrt{5})=a^2-5b^2$ is prime in $\mathbb{Z}$

Definition and evaluation of polynomial functions

finding the elements of equivalence class that contains $(-5,8)$ on the relation $\sim$ in $D\times S$ as follows

What is the reason to stipulate $0 \neq 1$ in the definition of Ordered Integral Domains?

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