Question

are the integers modulo 4 a field?

score 13.9k · Answer 1 · 2026-04-13 16:50:43

13.9k

Views

are the integers modulo 4 a field?

Published on 13 Apr 2026 - 16:50

score 595 · Answer 2 · 2026-04-14 11:53:57

595

Views

Proof-method: Show that if $n$ is not prime then $\Bbb Z /n\Bbb Z$ is not a field

Published on 14 Apr 2026 - 11:53

score 170 · Answer 3 · 2026-04-24 20:53:27

170

Views

Vector spaces over fields other than $\mathbb{R}$, $\mathbb{C}$, & $\mathbb{F}_{p^m}$

Published on 24 Apr 2026 - 20:53

score 1.1k · Answer 4 · 2026-04-10 21:41:03

1.1k

Views

Algebraic numbers, their minimal polynomial, and integer coefficients

Published on 10 Apr 2026 - 21:41

score 343 · Answer 5 · 2026-04-13 21:47:52

343

Views

Let f be an automorphism of some integral domain R. Show that f admits a unique extension to an automorphism of the quotient field.

Published on 13 Apr 2026 - 21:47

score 430 · Answer 6 · 2026-04-13 12:28:38

430

Views

When two primitive elements of a simple field extension are conjugate?

Published on 13 Apr 2026 - 12:28

score 292 · Answer 7 · 2026-04-12 02:17:59

292

Views

Square class of algebraic extension of finite fields

Published on 12 Apr 2026 - 2:17

score 208 · Answer 8 · 2026-04-17 21:58:57

208

Views

$\left[\Bbb{Q}\left(\cos\left({2\pi\over n}\right)+i\sin\left({2\pi\over n}\right)\right):\Bbb{Q}\right]=\phi(n)$

Published on 17 Apr 2026 - 21:58

score 86 · Answer 9 · 2026-04-14 21:21:21

86

Views

Algebraic closures and monomorphisms

Published on 14 Apr 2026 - 21:21

score 82 · Answer 10 · 2026-04-13 08:41:16

82

Views

Why the following field isn't an ordered field?

Published on 13 Apr 2026 - 8:41

score 511 · Answer 11 · 2026-04-15 06:22:22

511

Views

In a finite field $x^2 = a$ has at most two roots.

Published on 15 Apr 2026 - 6:22

score 1k · Answer 12 · 2026-04-11 00:24:55

1k

Views

Are natural numbers a field with alternate addition and multiplication

Published on 11 Apr 2026 - 0:24

score 191 · Answer 13 · 2026-04-17 20:04:51

191

Views

Discrete valuations on algebraic function fields: an additional condition that I don't understand

Published on 17 Apr 2026 - 20:04

score 49 · Answer 14 · 2026-04-11 04:07:08

49

Views

What is the relationship between non-repeated factors of the order of a group and its cyclicity?

Published on 11 Apr 2026 - 4:07

score 191 · Answer 15 · 2026-04-12 00:51:34

191

Views

Fields on uncountable sets

Published on 12 Apr 2026 - 0:51

List Question

are the integers modulo 4 a field?

Proof-method: Show that if $n$ is not prime then $\Bbb Z /n\Bbb Z$ is not a field

Vector spaces over fields other than $\mathbb{R}$, $\mathbb{C}$, & $\mathbb{F}_{p^m}$

Algebraic numbers, their minimal polynomial, and integer coefficients

Let f be an automorphism of some integral domain R. Show that f admits a unique extension to an automorphism of the quotient field.

When two primitive elements of a simple field extension are conjugate?

Square class of algebraic extension of finite fields

$\left[\Bbb{Q}\left(\cos\left({2\pi\over n}\right)+i\sin\left({2\pi\over n}\right)\right):\Bbb{Q}\right]=\phi(n)$

Algebraic closures and monomorphisms

Why the following field isn't an ordered field?

In a finite field $x^2 = a$ has at most two roots.

Are natural numbers a field with alternate addition and multiplication

Discrete valuations on algebraic function fields: an additional condition that I don't understand

What is the relationship between non-repeated factors of the order of a group and its cyclicity?

Fields on uncountable sets

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