Question

Prove $Z_{p}$ are prime fields,where $p$ is prime numbers

score 2k · Answer 1 · 2014-06-30 14:39:41

2k

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Prove $Z_{p}$ are prime fields,where $p$ is prime numbers

Published on 30 Jun 2014 - 14:39

score 116 · Answer 2 · 2026-03-30 17:09:58

116

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If $X^{p^d}\equiv X\text{ mod }f$ for prime numbers $p,d$, then $f\in\mathbb{F}_p[X]$ with $\deg f=d$ is irreducible over $\mathbb{F}_p$

Published on 30 Mar 2026 - 17:09

score 606 · Answer 3 · 2026-03-25 15:51:51

606

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If the localization of a ring is a field, then the ring is an integral domain?

Published on 25 Mar 2026 - 15:51

score 664 · Answer 4 · 2026-04-11 16:51:15

664

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What is the left adjoint of the forgetful functor from fields to integral domains?

Published on 11 Apr 2026 - 16:51

score 327 · Answer 5 · 2026-03-26 02:53:43

327

Views

Hensels Lemma in many variables

Published on 26 Mar 2026 - 2:53

score 490 · Answer 6 · 2014-07-02 01:43:24

490

Views

Is there a 'conjugation' on every algebraically closed field?

Published on 02 Jul 2014 - 1:43

score 45 · Answer 7 · 2026-04-12 06:46:07

45

Views

A request for a particular example in field theory.

Published on 12 Apr 2026 - 6:46

score 838 · Answer 8 · 2026-04-03 23:02:59

838

Views

Normalizer of a subgroup of a Galois group

Published on 03 Apr 2026 - 23:02

score 99 · Answer 9 · 2026-04-08 20:33:34

99

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A prime ideal in the intersection of powers of another ideal

Published on 08 Apr 2026 - 20:33

score 4.1k · Answer 10 · 2026-03-30 17:09:58

4.1k

Views

Let F be a field of order 32. Show that the only subfields of F are F itself and {0,1}.

Published on 30 Mar 2026 - 17:09

score 3k · Answer 11 · 2026-03-30 17:11:35

3k

Views

If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.

Published on 30 Mar 2026 - 17:11

score 27.1k · Answer 12 · 2026-04-09 12:42:19

27.1k

Views

What is Abstract Algebra essentially?

Published on 09 Apr 2026 - 12:42

score 41 · Answer 13 · 2026-04-11 21:38:07

41

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Field Isomorphisms between a field and something that contains it

Published on 11 Apr 2026 - 21:38

score 469 · Answer 14 · 2014-07-04 05:10:29

469

Views

Dimension of $\Bbb Q(e)$ over $\Bbb Q$?

Published on 04 Jul 2014 - 5:10

score 130 · Answer 15 · 2014-07-05 03:07:31

130

Views

A field extension of degree 8

Published on 05 Jul 2014 - 3:07

List Question

Prove $Z_{p}$ are prime fields,where $p$ is prime numbers

If $X^{p^d}\equiv X\text{ mod }f$ for prime numbers $p,d$, then $f\in\mathbb{F}_p[X]$ with $\deg f=d$ is irreducible over $\mathbb{F}_p$

If the localization of a ring is a field, then the ring is an integral domain?

What is the left adjoint of the forgetful functor from fields to integral domains?

Hensels Lemma in many variables

Is there a 'conjugation' on every algebraically closed field?

A request for a particular example in field theory.

Normalizer of a subgroup of a Galois group

A prime ideal in the intersection of powers of another ideal

Let F be a field of order 32. Show that the only subfields of F are F itself and {0,1}.

If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.

What is Abstract Algebra essentially?

Field Isomorphisms between a field and something that contains it

Dimension of $\Bbb Q(e)$ over $\Bbb Q$?

A field extension of degree 8

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