Question

Sharp's Exercise 13.35

score 51 · Answer 1 · 2018-06-26 14:19:56

51

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Sharp's Exercise 13.35

Published on 26 Jun 2018 - 14:19

score 97 · Answer 2 · 2018-06-29 06:43:57

97

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On the subring $k + Y k [X,Y]$ of the polynomial ring $k[X,Y]$

Published on 29 Jun 2018 - 6:43

score 202 · Answer 3 · 2018-09-01 12:59:48

202

Views

About the definition of an integral element in commutative rings

Published on 01 Sep 2018 - 12:59

score 70 · Answer 4 · 2018-09-09 21:15:33

70

Views

$A$ is a domain, $Q$ a prime ideal of $A$; connection between integral closedness of $A_Q$ and $A[X]_{Q[X]}$

Published on 09 Sep 2018 - 21:15

score 529 · Answer 5 · 2018-10-23 01:08:58

529

Views

If sum and product of elements are integral, they must be integral

Published on 23 Oct 2018 - 1:08

score 173 · Answer 6 · 2018-10-27 13:53:06

173

Views

Is an integer extension of a ring the integral closure of this ring in some extension?

Published on 27 Oct 2018 - 13:53

score 387 · Answer 7 · 2018-11-01 17:25:01

387

Views

Contraction of (non-prime) ideals in integral extensions

Published on 01 Nov 2018 - 17:25

score 51 · Answer 8 · 2018-11-12 07:34:31

Showing that $A[x] \cap A[x^{-1}] $ is an integral extension of $A$ when $x$ is invertible and $x$ belongs to a bigger ring containing $A$

score 93 · Answer 9 · 2018-12-01 23:14:34

93

Views

Noetherian domain whose fraction field is such that some specific proper submodules are projective

Published on 01 Dec 2018 - 23:14

score 62 · Answer 10 · 2018-12-16 18:33:25

62

Views

Conceptual reason for some formal properties of integral morphisms of rings

Published on 16 Dec 2018 - 18:33

score 94 · Answer 11 · 2018-12-22 23:58:49

94

Views

Geometry of the subalgebra $\Bbbk[x^2-1]\leq \Bbbk[x]$ (intuition for integral elements)

Published on 22 Dec 2018 - 23:58

score 174 · Answer 12 · 2018-12-31 01:25:06

174

Views

Infinite Noetherian ring of dimension $1$ in which distinct non-zero ideals have distinct and finite index

Published on 31 Dec 2018 - 1:25

score 79 · Answer 13 · 2019-01-09 23:47:06

79

Views

If $x$ is algebraic over a quotient field $K$ of $A$, then there exists an integral element $cx$ for some $A \ni c \neq 0$.

Published on 09 Jan 2019 - 23:47

score 235 · Answer 14 · 2019-01-24 22:27:50

235

Views

On integral closedness of formal power series ring over an integrally closed domain satisfying Krull intersection principle

Published on 24 Jan 2019 - 22:27

score 52 · Answer 15 · 2019-01-27 13:37:32

52

Views

When is $F[X]/(f)$ over $F$ an integral extension?

Published on 27 Jan 2019 - 13:37

List Question

Sharp's Exercise 13.35

On the subring $k + Y k [X,Y]$ of the polynomial ring $k[X,Y]$

About the definition of an integral element in commutative rings

$A$ is a domain, $Q$ a prime ideal of $A$; connection between integral closedness of $A_Q$ and $A[X]_{Q[X]}$

If sum and product of elements are integral, they must be integral

Is an integer extension of a ring the integral closure of this ring in some extension?

Contraction of (non-prime) ideals in integral extensions

Showing that $A[x] \cap A[x^{-1}] $ is an integral extension of $A$ when $x$ is invertible and $x$ belongs to a bigger ring containing $A$

Noetherian domain whose fraction field is such that some specific proper submodules are projective

Conceptual reason for some formal properties of integral morphisms of rings

Geometry of the subalgebra $\Bbbk[x^2-1]\leq \Bbbk[x]$ (intuition for integral elements)

Infinite Noetherian ring of dimension $1$ in which distinct non-zero ideals have distinct and finite index

If $x$ is algebraic over a quotient field $K$ of $A$, then there exists an integral element $cx$ for some $A \ni c \neq 0$.

On integral closedness of formal power series ring over an integrally closed domain satisfying Krull intersection principle

When is $F[X]/(f)$ over $F$ an integral extension?

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