Question

For a finite extension $K/F$ of degree $>1$, prove that $K$ is not the union of finitely many proper intermediate fields.

score 238 · Answer 1 · 2018-03-30 10:25:29

238

Views

For a finite extension $K/F$ of degree $>1$, prove that $K$ is not the union of finitely many proper intermediate fields.

Published on 30 Mar 2018 - 10:25

score 52 · Answer 2 · 2018-03-30 16:45:29

52

Views

Degree of Extensions

Published on 30 Mar 2018 - 16:45

score 46 · Answer 3 · 2018-03-30 17:08:29

46

Views

Characteristic fields and extensions

Published on 30 Mar 2018 - 17:08

score 39 · Answer 4 · 2018-03-30 19:34:50

39

Views

Extensions of a field

Published on 30 Mar 2018 - 19:34

score 198 · Answer 5 · 2018-03-31 17:21:35

198

Views

Show that $F [\alpha,\beta]$ is a field if $\alpha$ and $\beta$ are algebraic over $F$.

Published on 31 Mar 2018 - 17:21

score 52 · Answer 6 · 2018-04-01 05:34:04

52

Views

Show that $k (X)/k$ is not algebraic.

Published on 01 Apr 2018 - 5:34

score 216 · Answer 7 · 2018-04-01 16:27:34

216

Views

Smallest subfield containing F and {a}

Published on 01 Apr 2018 - 16:27

score 148 · Answer 8 · 2018-04-01 21:35:31

148

Views

Why is $\beta$ transcendental over $K$?

Published on 01 Apr 2018 - 21:35

score 79 · Answer 9 · 2018-04-02 13:50:48

79

Views

Given a field $K$, for which separable $\alpha,\beta$ do we have $[K(\alpha,\beta):K]=[K(\alpha):K]\cdot [K(\beta):K]$?

Published on 02 Apr 2018 - 13:50

score 2.3k · Answer 10 · 2018-04-03 00:52:46

2.3k

Views

Why do people study algebraic extension?

Published on 03 Apr 2018 - 0:52

score 66 · Answer 11 · 2026-03-17 07:08:09

66

Views

The maximal real algebraic field

Published on 17 Mar 2026 - 7:08

score 253 · Answer 12 · 2018-04-04 00:44:46

253

Views

Evaluation map in field extensions. $F$-algebra homomorphism.

Published on 04 Apr 2018 - 0:44

score 137 · Answer 13 · 2018-04-04 01:46:22

137

Views

Finite extension, linear transformation and minimal polynomial.

Published on 04 Apr 2018 - 1:46

score 338 · Answer 14 · 2018-04-04 11:59:06

338

Views

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

Published on 04 Apr 2018 - 11:59

score 73 · Answer 15 · 2018-04-05 03:39:45

73

Views

Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

Published on 05 Apr 2018 - 3:39

List Question

For a finite extension $K/F$ of degree $>1$, prove that $K$ is not the union of finitely many proper intermediate fields.

Degree of Extensions

Characteristic fields and extensions

Extensions of a field

Show that $F [\alpha,\beta]$ is a field if $\alpha$ and $\beta$ are algebraic over $F$.

Show that $k (X)/k$ is not algebraic.

Smallest subfield containing F and {a}

Why is $\beta$ transcendental over $K$?

Given a field $K$, for which separable $\alpha,\beta$ do we have $[K(\alpha,\beta):K]=[K(\alpha):K]\cdot [K(\beta):K]$?

Why do people study algebraic extension?

The maximal real algebraic field

Evaluation map in field extensions. $F$-algebra homomorphism.

Finite extension, linear transformation and minimal polynomial.

Why is $K[\alpha]$ a polynomial ring and the smallest subring containing $K$ and $\alpha$ of $L$?

Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

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