Question

If $x$ is integral over $A_m$ for all maximal ideals $m$, then $x$ is integral over $A$

score 152 · Answer 1 · 2014-01-24 22:04:17

152

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If $x$ is integral over $A_m$ for all maximal ideals $m$, then $x$ is integral over $A$

Published on 24 Jan 2014 - 22:04

score 112 · Answer 2 · 2014-01-25 19:05:48

112

Views

Show that $\operatorname{Spec}k[x_1,x_2,...,x_n]/(x_1^2+\cdots+x_m^2)$ is normal for $\operatorname{char}k\neq 2, n\ge m \ge 3$

Published on 25 Jan 2014 - 19:05

score 444 · Answer 3 · 2014-01-27 09:46:46

444

Views

Is the ring $\mathbb{C}[t^2,t^3]$ integrally closed?

Published on 27 Jan 2014 - 9:46

score 153 · Answer 4 · 2014-02-02 02:58:28

153

Views

Integral ring extension

Published on 02 Feb 2014 - 2:58

score 2.4k · Answer 5 · 2014-02-07 22:36:15

2.4k

Views

Is the integral closure of an integrally closed Noetherian domain in a finite extension field Noetherian?

Published on 07 Feb 2014 - 22:36

score 1.5k · Answer 6 · 2014-02-14 14:44:07

1.5k

Views

Integral dependence over rings is transitive

Published on 14 Feb 2014 - 14:44

score 308 · Answer 7 · 2014-02-14 15:15:01

308

Views

Ring of integers of $\mathbb{Q}(\omega_p,\omega_q)$

Published on 14 Feb 2014 - 15:15

score 3.4k · Answer 8 · 2014-02-16 13:34:07

3.4k

Views

Normalization of a quotient ring of polynomial rings (Reid, Exercise 4.6)

Published on 16 Feb 2014 - 13:34

score 958 · Answer 9 · 2014-03-06 15:32:13

958

Views

$k[X]$ is integral over $k[X^{2}]$

Published on 06 Mar 2014 - 15:32

score 1.1k · Answer 10 · 2026-03-03 18:06:23

1.1k

Views

Going Up Theorem - Examples? Witnesses?

Published on 03 Mar 2026 - 18:06

score 1.4k · Answer 11 · 2011-10-18 14:25:49

1.4k

Views

Quotient Rings and Integral Extensions

Published on 18 Oct 2011 - 14:25

score 11.4k · Answer 12 · 2012-01-17 18:58:33

11.4k

Views

Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$

Published on 17 Jan 2012 - 18:58

score 9.7k · Answer 13 · 2012-05-27 23:51:09

9.7k

Views

UFDs are integrally closed; so too are GCD & Dedekind domains.

Published on 27 May 2012 - 23:51

score 602 · Answer 14 · 2012-10-26 18:46:53

602

Views

If the complement of a subring is closed under multiplication, then the subring is integrally closed.

Published on 26 Oct 2012 - 18:46

score 436 · Answer 15 · 2013-01-08 11:30:52

436

Views

Integral extension (Exercise 4.9, M. Reid, Undergraduate Commutative Algebra)

Published on 08 Jan 2013 - 11:30

List Question

If $x$ is integral over $A_m$ for all maximal ideals $m$, then $x$ is integral over $A$

Show that $\operatorname{Spec}k[x_1,x_2,...,x_n]/(x_1^2+\cdots+x_m^2)$ is normal for $\operatorname{char}k\neq 2, n\ge m \ge 3$

Is the ring $\mathbb{C}[t^2,t^3]$ integrally closed?

Integral ring extension

Is the integral closure of an integrally closed Noetherian domain in a finite extension field Noetherian?

Integral dependence over rings is transitive

Ring of integers of $\mathbb{Q}(\omega_p,\omega_q)$

Normalization of a quotient ring of polynomial rings (Reid, Exercise 4.6)

$k[X]$ is integral over $k[X^{2}]$

Going Up Theorem - Examples? Witnesses?

Quotient Rings and Integral Extensions

Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$

UFDs are integrally closed; so too are GCD & Dedekind domains.

If the complement of a subring is closed under multiplication, then the subring is integrally closed.

Integral extension (Exercise 4.9, M. Reid, Undergraduate Commutative Algebra)

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