List questions from integral-extensions

Published on 07 Feb 2021 - 10:07

569

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How to prove that UFD implies normal?

Published on 30 Mar 2026 - 12:19

36

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Do quotienting and contraction commute?

Published on 23 Feb 2021 - 13:40

101

Views

Algebraically closed proof.

Published on 27 Mar 2026 - 18:05

60

Views

Units, determinants and irreducibility.

Published on 24 Feb 2021 - 4:37

331

Views

Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.

Published on 25 Feb 2021 - 17:33

68

Views

Field Extensions with Common Transcendental Numbers

Published on 26 Mar 2026 - 8:15

232

Views

Showing that the intersection of two sets is integral

Published on 23 Feb 2026 - 13:42

41

Views

Integral closure of $A \subseteq B$ is a subring of $B$

Published on 12 Apr 2021 - 3:17

139

Views

Question about Going down theorem in Gopalakrishnan

Published on 04 Jul 2021 - 23:46

80

Views

Universal splitting algebra of a monic polynomial over a field is a field?

Published on 29 Mar 2026 - 17:44

208

Views

$R/xR$ normal domain then $R$ is also a normal domain

Published on 03 Sep 2021 - 22:38

82

Views

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

Published on 29 Mar 2026 - 13:24

54

Views

If $R\subseteq S$ is a split extension of Noetherian domains and $S$ is normal, then is $R$ normal?

Published on 29 Mar 2026 - 20:51

261

Views

Is there an integral extension of $\mathbb{Z}$ keeping its prime elements?

Published on 23 Feb 2026 - 16:24

List Question

Proving that the integral closure of $R$ in $S$ is a subring of $S.$

How to prove that UFD implies normal?

Do quotienting and contraction commute?

Algebraically closed proof.

Units, determinants and irreducibility.

Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.

Field Extensions with Common Transcendental Numbers

Showing that the intersection of two sets is integral

Integral closure of $A \subseteq B$ is a subring of $B$

Question about Going down theorem in Gopalakrishnan

Universal splitting algebra of a monic polynomial over a field is a field?

$R/xR$ normal domain then $R$ is also a normal domain

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

If $R\subseteq S$ is a split extension of Noetherian domains and $S$ is normal, then is $R$ normal?

Is there an integral extension of $\mathbb{Z}$ keeping its prime elements?

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