Question

There is exactly one algebraically closed field with prescribed characteristic and cardinality

score 930 · Answer 1 · 2018-04-27 15:52:13

930

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There is exactly one algebraically closed field with prescribed characteristic and cardinality

Published on 27 Apr 2018 - 15:52

score 1.1k · Answer 2 · 2026-03-22 09:00:28

1.1k

Views

Let $L/K$ be a finite separable field extension. How to prove there are finitely many intermediate fields?

Published on 22 Mar 2026 - 9:00

score 3.2k · Answer 3 · 2018-04-28 20:25:42

3.2k

Views

Understanding an Algebra over a Field

Published on 28 Apr 2018 - 20:25

score 308 · Answer 4 · 2026-03-26 04:51:11

308

Views

Field with both $\mathbb{Z}/{5}$ and $\mathbb{Z}/{7}$ as subfields?

Published on 26 Mar 2026 - 4:51

score 59 · Answer 5 · 2018-04-28 23:29:22

59

Views

Clarification on Polynomial operations

Published on 28 Apr 2018 - 23:29

score 452 · Answer 6 · 2026-03-26 13:02:18

452

Views

Finding zeros of $x^{86}-6$ over the field $Z_{29}$ (abstract algebra)

Published on 26 Mar 2026 - 13:02

score 46 · Answer 7 · 2018-04-29 16:06:49

46

Views

Polynomials with degree of 3 having real root iff the discriminant of the polynom is non negative

Published on 29 Apr 2018 - 16:06

score 631 · Answer 8 · 2026-03-25 07:40:55

631

Views

Using model theory to prove a Real Nullstellensatz?

Published on 25 Mar 2026 - 7:40

score 195 · Answer 9 · 2026-03-22 23:20:08

195

Views

Are normal extensions always simple?

Published on 22 Mar 2026 - 23:20

score 92 · Answer 10 · 2026-03-25 17:26:58

92

Views

Show that if A is algebraic closure of F and K is an intermediate field, then A is also the algebraic closure of K. Confirm solution?

Published on 25 Mar 2026 - 17:26

score 179 · Answer 11 · 2026-03-25 17:17:23

179

Views

On Galois intersection

Published on 25 Mar 2026 - 17:17

score 262 · Answer 12 · 2026-03-26 03:13:28

262

Views

The number of elements $ \alpha $ we can adjoin to a finite field $ F $ to obtain an extension field.

Published on 26 Mar 2026 - 3:13

score 67 · Answer 13 · 2026-03-25 17:25:00

67

Views

Set generated by all finite field operations.

Published on 25 Mar 2026 - 17:25

score 71 · Answer 14 · 2026-03-25 17:18:46

71

Views

How to make a field extension chain

Published on 25 Mar 2026 - 17:18

score 504 · Answer 15 · 2018-04-30 21:09:52

504

Views

The relation between integral domains and their field of fractions.

Published on 30 Apr 2018 - 21:09

List Question

There is exactly one algebraically closed field with prescribed characteristic and cardinality

Let $L/K$ be a finite separable field extension. How to prove there are finitely many intermediate fields?

Understanding an Algebra over a Field

Field with both $\mathbb{Z}/{5}$ and $\mathbb{Z}/{7}$ as subfields?

Clarification on Polynomial operations

Finding zeros of $x^{86}-6$ over the field $Z_{29}$ (abstract algebra)

Polynomials with degree of 3 having real root iff the discriminant of the polynom is non negative

Using model theory to prove a Real Nullstellensatz?

Are normal extensions always simple?

Show that if A is algebraic closure of F and K is an intermediate field, then A is also the algebraic closure of K. Confirm solution?

On Galois intersection

The number of elements $ \alpha $ we can adjoin to a finite field $ F $ to obtain an extension field.

Set generated by all finite field operations.

How to make a field extension chain

The relation between integral domains and their field of fractions.

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