List questions from extension-field

Published on 29 Mar 2026 - 14:00

282

Views

Show that if Y is transcendental over a field K, and F is a field with $K\subset F\subset K(Y)$ and $K\neq F$ then Y is algebraic on F

Published on 03 Jul 2019 - 22:25

33

Views

Containment of $\mathbb Q(a)$

Published on 04 Jul 2019 - 15:52

428

Views

Is every subextension of a simple field extension simple itself?

Published on 06 Jul 2019 - 17:39

1.3k

Views

If every polynomial in $k[x]$ has a root in $E$, is $E$ algebraically closed?

Published on 06 Jul 2019 - 22:34

557

Views

Minimal polynomial of $\sqrt{2+\sqrt[3]{3}}$ over $\mathbb{Q}$

Published on 07 Jul 2019 - 8:05

313

Views

Extension of scalars for a $k$-scheme

Published on 29 Mar 2026 - 18:33

52

Views

Conjecture about extending a field

Published on 08 Jul 2019 - 18:36

51

Views

Is $ [\Bbb Q(\pi):\Bbb Q]$ finite?

Published on 09 Jul 2019 - 8:07

63

Views

Field extensions, stupid question

Published on 10 Jul 2019 - 9:42

130

Views

Adjoining elements in subextension

Published on 10 Jul 2019 - 15:56

163

Views

Geometrically Reduced implies Reduced (resp geom. Integral, Irreducible)

Published on 29 Mar 2026 - 18:31

395

Views

When (if ever) is a field extension a tensor product of intermediate extensions?

Published on 12 Jul 2019 - 6:03

235

Views

If $E/F$ is a field extension of degree $2$ and $\text{char}(F)\ne 2$ then $E=F(\sqrt a)$ for some $a\in E$

Published on 27 Mar 2026 - 7:16

49

Views

If $E/F$ is a field extension with $a,b\in E$ of "degree" $n,m$ then $ab$ and $a+b$ have "degree" less then $mn$

Published on 27 Mar 2026 - 7:16

List Question

Minimal polynomial over a field extension

Show that if Y is transcendental over a field K, and F is a field with $K\subset F\subset K(Y)$ and $K\neq F$ then Y is algebraic on F

Containment of $\mathbb Q(a)$

Is every subextension of a simple field extension simple itself?

If every polynomial in $k[x]$ has a root in $E$, is $E$ algebraically closed?

Minimal polynomial of $\sqrt{2+\sqrt[3]{3}}$ over $\mathbb{Q}$

Extension of scalars for a $k$-scheme

Conjecture about extending a field

Is $ [\Bbb Q(\pi):\Bbb Q]$ finite?

Field extensions, stupid question

Adjoining elements in subextension

Geometrically Reduced implies Reduced (resp geom. Integral, Irreducible)

When (if ever) is a field extension a tensor product of intermediate extensions?

If $E/F$ is a field extension of degree $2$ and $\text{char}(F)\ne 2$ then $E=F(\sqrt a)$ for some $a\in E$

If $E/F$ is a field extension with $a,b\in E$ of "degree" $n,m$ then $ab$ and $a+b$ have "degree" less then $mn$

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