Question

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

score 1k · Answer 1 · 2015-06-24 00:30:31

1k

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

Published on 24 Jun 2015 - 0:30

score 72 · Answer 2 · 2015-07-22 16:06:06

72

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

Published on 22 Jul 2015 - 16:06

score 454 · Answer 3 · 2015-09-15 10:31:35

454

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

Published on 15 Sep 2015 - 10:31

score 75 · Answer 4 · 2015-09-20 13:51:27

75

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Find a monic polynomial

Published on 20 Sep 2015 - 13:51

score 305 · Answer 5 · 2015-09-24 17:25:13

305

Views

Gaussian Integer is Integral Over Integer

Published on 24 Sep 2015 - 17:25

score 865 · Answer 6 · 2015-10-05 11:32:14

865

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

Published on 05 Oct 2015 - 11:32

score 607 · Answer 7 · 2015-11-14 19:03:18

607

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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 14 Nov 2015 - 19:03

score 284 · Answer 8 · 2015-11-24 14:34:50

284

Views

Equivalent conditions for integral element

Published on 24 Nov 2015 - 14:34

score 974 · Answer 9 · 2026-03-19 06:27:21

974

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

Published on 19 Mar 2026 - 6:27

score 618 · Answer 10 · 2016-01-13 01:42:29

618

Views

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

Published on 13 Jan 2016 - 1:42

score 952 · Answer 11 · 2016-02-25 13:59:36

952

Views

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

Published on 25 Feb 2016 - 13:59

score 4.8k · Answer 12 · 2013-09-21 12:49:45

4.8k

Views

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

Published on 21 Sep 2013 - 12:49

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 78 · Answer 14 · 2013-12-03 23:36:33

78

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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 03 Dec 2013 - 23:36

score 380 · Answer 15 · 2014-01-05 22:29:16

380

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 05 Jan 2014 - 22:29

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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