List questions from integral-dependence

Published on 26 Feb 2026 - 10:48

88

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Let $A\subset B$ be an integral ring extension, and $p\in\operatorname{Spec}A$. Then there exists $q\in\operatorname{Spec}B$ such that $q\cap A=p$.

Published on 24 Nov 2019 - 23:46

295

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Integral Dependence

Published on 22 Mar 2026 - 3:31

431

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Integral closure of Gaussian Integers

Published on 08 Jul 2016 - 19:26

270

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Let $k$ be a field of characteristic $\neq 2$, and $n\geq m\geq 3$. Then $k[x_1,\ldots,x_n]/\langle x_1^2+\ldots+x_m^2\rangle$ is integrally closed.

Published on 07 Aug 2016 - 22:10

89

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Domain without any non trivial integral extensions (any monic polynomial $f \in A[x] \setminus \{1\}$ has a root in $A$) is a field?

Published on 04 Dec 2016 - 21:05

40

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$A$ subring of $B$, $p_2\subseteq p_1$ prime ideals in $A$ and $q_1$ prime ideal in $B$ such that $p_1=q_1\cap B$ then $p_2^e=B_{q_1}p_2$

Published on 12 Jul 2023 - 11:36

105

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Intuitive Meaning of Integral Dependence

Published on 10 Sep 2023 - 9:25

80

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Show that $\alpha_i$ are integral over $k[x]$ and generate the integral closure over $k[x]$.

Published on 28 Oct 2023 - 15:07

544

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Integral extension is a finitely generated $R$-module?

Published on 31 Jan 2015 - 17:03

606

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Extension of Integral Domains

Published on 18 Mar 2015 - 19:30

94

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Which type of correlation should I use?

Published on 21 Apr 2015 - 12:50

194

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Is the preimage of the non-normal locus a divisor?

Published on 21 Apr 2015 - 15:08

217

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Show that $B/Q$ is integral over $A/P$

Published on 26 Apr 2015 - 7:19

257

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Extending an automorphism to the integral closure

Published on 11 May 2015 - 17:58

List Question

Every element of a ring $A$ is integral over the ring $A$. How?

Let $A\subset B$ be an integral ring extension, and $p\in\operatorname{Spec}A$. Then there exists $q\in\operatorname{Spec}B$ such that $q\cap A=p$.

Integral Dependence

Integral closure of Gaussian Integers

Let $k$ be a field of characteristic $\neq 2$, and $n\geq m\geq 3$. Then $k[x_1,\ldots,x_n]/\langle x_1^2+\ldots+x_m^2\rangle$ is integrally closed.

Domain without any non trivial integral extensions (any monic polynomial $f \in A[x] \setminus \{1\}$ has a root in $A$) is a field?

$A$ subring of $B$, $p_2\subseteq p_1$ prime ideals in $A$ and $q_1$ prime ideal in $B$ such that $p_1=q_1\cap B$ then $p_2^e=B_{q_1}p_2$

Intuitive Meaning of Integral Dependence

Show that $\alpha_i$ are integral over $k[x]$ and generate the integral closure over $k[x]$.

Integral extension is a finitely generated $R$-module?

Extension of Integral Domains

Which type of correlation should I use?

Is the preimage of the non-normal locus a divisor?

Show that $B/Q$ is integral over $A/P$

Extending an automorphism to the integral closure

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