Question

Showing that $k[x]$ is integral over $k[x^2-1]$

score 39 · Answer 1 · 2023-09-28 08:33:03

39

Views

Showing that $k[x]$ is integral over $k[x^2-1]$

Published on 28 Sep 2023 - 8:33

score 76 · Answer 2 · 2023-10-18 02:46:38

76

Views

The notion of "units" is independent of the base algebraic integer ring.

Published on 18 Oct 2023 - 2:46

score 61 · Answer 3 · 2023-11-01 17:02:41

61

Views

Integral elements over an ideal in an integrally closed domain and the minimal polynomial over the field of fractions

Published on 01 Nov 2023 - 17:02

score 83 · Answer 4 · 2023-11-27 23:53:59

83

Views

Is this Proof on Integral Element Valid?

Published on 27 Nov 2023 - 23:53

score 56 · Answer 5 · 2023-11-29 17:24:02

56

Views

Could You help me Clarify this Solution on Integral Extension?

Published on 29 Nov 2023 - 17:24

score 65 · Answer 6 · 2024-01-22 11:28:47

65

Views

Going-up theorem: isn't it an obvious corollary of Theorem 5.10 (Atiyah)?

Published on 22 Jan 2024 - 11:28

score 80 · Answer 7 · 2024-03-10 20:26:19

80

Views

If $A$ is a Jacobson ring, so is $A[X]$

Published on 10 Mar 2024 - 20:26

score 90 · Answer 8 · 2024-03-11 04:32:45

90

Views

Normality and integrality of schemes and splitting of map from structure sheaf to derived-pushforward of structure sheaf along proper birational map

Published on 11 Mar 2024 - 4:32

score 235 · Answer 9 · 2015-03-17 19:06:59

235

Views

Question about Subrings and integraly closed

Published on 17 Mar 2015 - 19:06

score 113 · Answer 10 · 2015-06-24 00:38:19

113

Views

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

Published on 24 Jun 2015 - 0:38

score 21 · Answer 11 · 2015-12-01 20:24:16

21

Views

$b w_i = \sum\limits_{i=1}^r a_{i,j} w_j \implies \det(bI - (a_{i,j})) w_i = 0$ in an $R$-module.

Published on 01 Dec 2015 - 20:24

score 48 · Answer 12 · 2015-12-01 21:30:45

48

Views

Understanding Jurgen Neukirch proof that $A[b_1, \dots, b_n]$ finitely generated $\implies$ it's integral over $A$.

Published on 01 Dec 2015 - 21:30

score 145 · Answer 13 · 2016-01-04 10:55:23

145

Views

How does $R/(R \cap I)$ sit inside of $S/I$, where $R \subset S$ is an integral extension.

Published on 04 Jan 2016 - 10:55

score 303 · Answer 14 · 2016-02-15 07:24:20

303

Views

Extension of ideals in integral extensions

Published on 15 Feb 2016 - 7:24

score 1.6k · Answer 15 · 2016-04-11 15:33:11

1.6k

Views

Field of fractions of integral extension is an algebraic extension

Published on 11 Apr 2016 - 15:33

List Question

Showing that $k[x]$ is integral over $k[x^2-1]$

The notion of "units" is independent of the base algebraic integer ring.

Integral elements over an ideal in an integrally closed domain and the minimal polynomial over the field of fractions

Is this Proof on Integral Element Valid?

Could You help me Clarify this Solution on Integral Extension?

Going-up theorem: isn't it an obvious corollary of Theorem 5.10 (Atiyah)?

If $A$ is a Jacobson ring, so is $A[X]$

Normality and integrality of schemes and splitting of map from structure sheaf to derived-pushforward of structure sheaf along proper birational map

Question about Subrings and integraly closed

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

$b w_i = \sum\limits_{i=1}^r a_{i,j} w_j \implies \det(bI - (a_{i,j})) w_i = 0$ in an $R$-module.

Understanding Jurgen Neukirch proof that $A[b_1, \dots, b_n]$ finitely generated $\implies$ it's integral over $A$.

How does $R/(R \cap I)$ sit inside of $S/I$, where $R \subset S$ is an integral extension.

Extension of ideals in integral extensions

Field of fractions of integral extension is an algebraic extension

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