Question

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

score 153 · Answer 1 · 2026-03-25 06:05:40

153

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

Published on 25 Mar 2026 - 6:05

score 113 · Answer 2 · 2026-03-25 07:46:31

113

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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 Mar 2026 - 7:46

score 445 · Answer 3 · 2026-03-25 06:08:20

445

Views

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

Published on 25 Mar 2026 - 6:08

score 155 · Answer 4 · 2026-04-10 06:57:47

155

Views

Integral ring extension

Published on 10 Apr 2026 - 6:57

score 2.4k · Answer 5 · 2026-03-25 06:06:18

2.4k

Views

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

Published on 25 Mar 2026 - 6:06

score 1.5k · Answer 6 · 2026-03-25 07:32:22

1.5k

Views

Integral dependence over rings is transitive

Published on 25 Mar 2026 - 7:32

score 309 · Answer 7 · 2026-03-25 06:04:17

309

Views

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

Published on 25 Mar 2026 - 6:04

score 3.4k · Answer 8 · 2026-03-25 06:04:44

3.4k

Views

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

Published on 25 Mar 2026 - 6:04

score 960 · Answer 9 · 2026-04-11 01:58:17

960

Views

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

Published on 11 Apr 2026 - 1:58

score 1.1k · Answer 10 · 2026-05-02 19:28:27

1.1k

Views

Going Up Theorem - Examples? Witnesses?

Published on 02 May 2026 - 19:28

score 1.4k · Answer 11 · 2026-04-10 23:05:08

1.4k

Views

Quotient Rings and Integral Extensions

Published on 10 Apr 2026 - 23:05

score 11.4k · Answer 12 · 2026-04-15 17:43:16

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 15 Apr 2026 - 17:43

score 9.7k · Answer 13 · 2026-04-16 06:14:37

9.7k

Views

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

Published on 16 Apr 2026 - 6:14

score 605 · Answer 14 · 2026-04-13 09:00:40

605

Views

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

Published on 13 Apr 2026 - 9:00

score 439 · Answer 15 · 2026-04-16 03:40:18

439

Views

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

Published on 16 Apr 2026 - 3:40

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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