Question

Integral extension of polynomial rings.

score 926 · Answer 1 · 2016-10-07 14:32:53

926

Views

Integral extension of polynomial rings.

Published on 07 Oct 2016 - 14:32

score 321 · Answer 2 · 2016-10-15 14:06:53

321

Views

Finite extension of domains : preimage of non-zero ideal is non-zero?

Published on 15 Oct 2016 - 14:06

score 790 · Answer 3 · 2016-11-19 11:12:19

790

Views

Contraction of extension of prime ideals in an integral ring extension

Published on 19 Nov 2016 - 11:12

score 250 · Answer 4 · 2016-11-28 16:42:46

250

Views

About localization of integral closure at maximal ideals.

Published on 28 Nov 2016 - 16:42

score 345 · Answer 5 · 2016-12-01 17:21:15

345

Views

Integral closure and algebraic closure

Published on 01 Dec 2016 - 17:21

score 256 · Answer 6 · 2017-01-26 01:15:28

256

Views

Normality of $\mathbb{C}[x, y]/(y^2-x^3+x)$

Published on 26 Jan 2017 - 1:15

score 49 · Answer 7 · 2017-03-05 05:29:30

49

Views

$S$ is a subring of an integral domain $R$ which is finitely generated algebra over $S$, Jac(S)=0 implies Jac(R)=0

Published on 05 Mar 2017 - 5:29

score 2.1k · Answer 8 · 2017-03-07 02:10:19

2.1k

Views

$R$ is integrally closed in $S$ iff $R[x]$ is integrally closed in $S[x]$

Published on 07 Mar 2017 - 2:10

score 621 · Answer 9 · 2017-03-15 05:49:17

621

Views

Checking whether a given element is integral over $\mathbb{Z}$.

Published on 15 Mar 2017 - 5:49

score 405 · Answer 10 · 2023-05-05 15:04:34

405

Views

If a polynomial in $B[x]$ is integral over $A[x]$, then are its coefficients integral over $A$?

Published on 05 May 2023 - 15:04

score 140 · Answer 11 · 2023-05-16 00:27:24

140

Views

Show $\mathbb{Z}\left[i,\frac{1+\sqrt{5}}{2}\right]$ is integrally closed

Published on 16 May 2023 - 0:27

score 58 · Answer 12 · 2023-06-25 12:46:54

58

Views

Understanding the proof of the existence of absolute integral closure

Published on 25 Jun 2023 - 12:46

score 68 · Answer 13 · 2023-07-17 12:13:14

68

Views

$1$-dimensional reduced local ring $R$ such that $(R:_{Q(R)} \overline R)$ is non-zero and consists of zero-divisors

Published on 17 Jul 2023 - 12:13

score 116 · Answer 14 · 2023-07-23 10:43:39

116

Views

$C$ is integral closure of $A$ then $C[x]$ is of $A[x]$

Published on 23 Jul 2023 - 10:43

score 48 · Answer 15 · 2023-09-16 20:05:05

48

Views

Show $\left(F\left[X_{1}, \ldots, X_{n}\right]\right)^{A_{n}}$ is an integral extension of $\left(F\left[X_{1}, \ldots, X_{n}\right]\right)^{S_{n}}$

Published on 16 Sep 2023 - 20:05

List Question

Integral extension of polynomial rings.

Finite extension of domains : preimage of non-zero ideal is non-zero?

Contraction of extension of prime ideals in an integral ring extension

About localization of integral closure at maximal ideals.

Integral closure and algebraic closure

Normality of $\mathbb{C}[x, y]/(y^2-x^3+x)$

$S$ is a subring of an integral domain $R$ which is finitely generated algebra over $S$, Jac(S)=0 implies Jac(R)=0

$R$ is integrally closed in $S$ iff $R[x]$ is integrally closed in $S[x]$

Checking whether a given element is integral over $\mathbb{Z}$.

If a polynomial in $B[x]$ is integral over $A[x]$, then are its coefficients integral over $A$?

Show $\mathbb{Z}\left[i,\frac{1+\sqrt{5}}{2}\right]$ is integrally closed

Understanding the proof of the existence of absolute integral closure

$1$-dimensional reduced local ring $R$ such that $(R:_{Q(R)} \overline R)$ is non-zero and consists of zero-divisors

$C$ is integral closure of $A$ then $C[x]$ is of $A[x]$

Show $\left(F\left[X_{1}, \ldots, X_{n}\right]\right)^{A_{n}}$ is an integral extension of $\left(F\left[X_{1}, \ldots, X_{n}\right]\right)^{S_{n}}$

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