Question

How to show that a finite commutative ring without zero divisors is a field?

score 16.7k · Answer 1 · 2026-04-12 12:21:22

16.7k

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How to show that a finite commutative ring without zero divisors is a field?

Published on 12 Apr 2026 - 12:21

score 111 · Answer 2 · 2026-04-12 17:11:23

111

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How can commuting with Frobenius imply the order of an element in the inertia group.

Published on 12 Apr 2026 - 17:11

score 156 · Answer 3 · 2026-04-09 13:36:13

156

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Field projection

Published on 09 Apr 2026 - 13:36

score 331 · Answer 4 · 2026-04-15 07:49:48

331

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Is there a field with $n$ elements for all $n \in \mathbb{N}$?

Published on 15 Apr 2026 - 7:49

score 774 · Answer 5 · 2026-04-12 02:09:35

774

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General advice on multiplying polynomials in a finite field?

Published on 12 Apr 2026 - 2:09

score 136 · Answer 6 · 2026-04-16 04:53:17

136

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Largest power of a prime dividing $q^m-1$

Published on 16 Apr 2026 - 4:53

score 138 · Answer 7 · 2026-04-14 04:25:31

138

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Polynomial restricts to zero on a hyperplane implies divisibility

Published on 14 Apr 2026 - 4:25

score 1.4k · Answer 8 · 2026-04-15 06:49:55

1.4k

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Using Hensel's Lemma to Factor a Polynomial over $\mathbb{Z}_4[x]$

Published on 15 Apr 2026 - 6:49

score 437 · Answer 9 · 2026-04-13 11:30:20

437

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Orientation on finite dimensional vector spaces over finite fields.

Published on 13 Apr 2026 - 11:30

score 1.3k · Answer 10 · 2026-04-13 01:20:15

1.3k

Views

finite field to rational fraction

Published on 13 Apr 2026 - 1:20

score 251 · Answer 11 · 2026-04-12 16:33:22

251

Views

On a characterization of primitive polynomials over a finite field

Published on 12 Apr 2026 - 16:33

score 432 · Answer 12 · 2026-04-15 23:17:05

432

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Subgroup structure of $\mathrm{SL}(2, p^2)$ and its irreducible characters

Published on 15 Apr 2026 - 23:17

score 110 · Answer 13 · 2026-04-14 14:38:12

110

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Prove that in $\mathbb{Z}_p$, $[a]^{-1} = [a]$ if and only if $[a]=[1]$ or $[a]=[p-1]$

Published on 14 Apr 2026 - 14:38

score 69 · Answer 14 · 2026-04-13 16:15:48

69

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Representing an element mod $n$ as a product of two primes

Published on 13 Apr 2026 - 16:15

score 460 · Answer 15 · 2026-04-28 15:16:48

460

Views

$E/\mathbb F_q$ extension field. Show $[\mathbb F_q(\alpha) : \mathbb F_q]$ is smallest $n$ satisfying property.

Published on 28 Apr 2026 - 15:16

List Question

How to show that a finite commutative ring without zero divisors is a field?

How can commuting with Frobenius imply the order of an element in the inertia group.

Field projection

Is there a field with $n$ elements for all $n \in \mathbb{N}$?

General advice on multiplying polynomials in a finite field?

Largest power of a prime dividing $q^m-1$

Polynomial restricts to zero on a hyperplane implies divisibility

Using Hensel's Lemma to Factor a Polynomial over $\mathbb{Z}_4[x]$

Orientation on finite dimensional vector spaces over finite fields.

finite field to rational fraction

On a characterization of primitive polynomials over a finite field

Subgroup structure of $\mathrm{SL}(2, p^2)$ and its irreducible characters

Prove that in $\mathbb{Z}_p$, $[a]^{-1} = [a]$ if and only if $[a]=[1]$ or $[a]=[p-1]$

Representing an element mod $n$ as a product of two primes

$E/\mathbb F_q$ extension field. Show $[\mathbb F_q(\alpha) : \mathbb F_q]$ is smallest $n$ satisfying property.

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