Question

Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?

score 1k · Answer 1 · 2026-03-25 04:40:15

1k

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Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?

Published on 25 Mar 2026 - 4:40

score 73 · Answer 2 · 2026-03-25 04:39:19

73

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Why do we need injectivity in the definition of integral dependence?

Published on 25 Mar 2026 - 4:39

score 455 · Answer 3 · 2026-03-25 04:39:21

455

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Show that $A[x] \cap A[x^{-1}]$ is integral over $A$.

Published on 25 Mar 2026 - 4:39

score 77 · Answer 4 · 2026-04-06 01:14:14

77

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Find a monic polynomial

Published on 06 Apr 2026 - 1:14

score 306 · Answer 5 · 2026-03-25 07:38:18

306

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Gaussian Integer is Integral Over Integer

Published on 25 Mar 2026 - 7:38

score 866 · Answer 6 · 2026-03-25 04:42:47

866

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Ring of fractions of an integrally closed integral domain is also integrally closed

Published on 25 Mar 2026 - 4:42

score 608 · Answer 7 · 2026-04-06 04:35:59

608

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$x$ is integral over $R$ if and only if for every minimal prime $\mathfrak q$ of $S$, $x$ is integral over the residue domains

Published on 06 Apr 2026 - 4:35

score 287 · Answer 8 · 2026-05-06 18:17:43

287

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Equivalent conditions for integral element

Published on 06 May 2026 - 18:17

score 975 · Answer 9 · 2026-04-18 12:33:43

975

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How to compute the integral closure of $\Bbb{Z}$ in $\mathbb Q(\sqrt[n]{p})$?

Published on 18 Apr 2026 - 12:33

score 619 · Answer 10 · 2026-04-23 12:53:02

619

Views

What is the integral closure of the integers in the real numbers?

Published on 23 Apr 2026 - 12:53

score 953 · Answer 11 · 2026-04-10 02:14:46

953

Views

Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$

Published on 10 Apr 2026 - 2:14

score 4.8k · Answer 12 · 2026-04-29 00:30:43

4.8k

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Working out the normalization of $\mathbb C[X,Y]/(X^2-Y^3)$

Published on 29 Apr 2026 - 0:30

score 807 · Answer 13 · 2013-11-30 09:22:24

807

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Hints about Exercise 4.2 in Miles Reid, Undergraduate Commutative Algebra

Published on 30 Nov 2013 - 9:22

score 79 · Answer 14 · 2026-03-25 04:43:43

79

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Necessity of an hypothesis in this exercise about integral dependence of $k[x][\frac{1}{f}]$ over $k[x]$

Published on 25 Mar 2026 - 4:43

score 381 · Answer 15 · 2026-03-25 04:43:49

381

Views

Consider $R[x]$ and let $S$ be the subring generated by $rx$, where $r \in R$ is some non-invertible element. Then $x$ is not integral over $S$

Published on 25 Mar 2026 - 4:43

List Question

Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?

Why do we need injectivity in the definition of integral dependence?

Show that $A[x] \cap A[x^{-1}]$ is integral over $A$.

Find a monic polynomial

Gaussian Integer is Integral Over Integer

Ring of fractions of an integrally closed integral domain is also integrally closed

$x$ is integral over $R$ if and only if for every minimal prime $\mathfrak q$ of $S$, $x$ is integral over the residue domains

Equivalent conditions for integral element

How to compute the integral closure of $\Bbb{Z}$ in $\mathbb Q(\sqrt[n]{p})$?

What is the integral closure of the integers in the real numbers?

Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$

Working out the normalization of $\mathbb C[X,Y]/(X^2-Y^3)$

Hints about Exercise 4.2 in Miles Reid, Undergraduate Commutative Algebra

Necessity of an hypothesis in this exercise about integral dependence of $k[x][\frac{1}{f}]$ over $k[x]$

Consider $R[x]$ and let $S$ be the subring generated by $rx$, where $r \in R$ is some non-invertible element. Then $x$ is not integral over $S$

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