Question

Let $K \subset L$ be a finite extension with $p = \text{char}(K) > 0.$ Prove $[L : K]_s \cdot p^k= [L : K]$ for $k \in \mathbb{Z}_{\geq 0}$.

score 232 · Answer 1 · 2026-04-14 22:02:44

232

Views

Let $K \subset L$ be a finite extension with $p = \text{char}(K) > 0.$ Prove $[L : K]_s \cdot p^k= [L : K]$ for $k \in \mathbb{Z}_{\geq 0}$.

Published on 14 Apr 2026 - 22:02

score 104 · Answer 2 · 2026-04-16 03:07:10

104

Views

Matrices over $\mathbb{F}_p$ satisfying a Determinant and Trace Condition

Published on 16 Apr 2026 - 3:07

score 37 · Answer 3 · 2026-04-17 11:03:53

37

Views

Let $p(x)$ be polynomial over $GF(2)$ with $deg(p(x))=8$, show that $g(x)\nmid x^{31}-1$

Published on 17 Apr 2026 - 11:03

score 78 · Answer 4 · 2026-04-15 23:08:37

78

Views

"smallest" irreducible polynomial over GF(p)

Published on 15 Apr 2026 - 23:08

score 77 · Answer 5 · 2026-04-15 09:20:31

77

Views

Cohomological dimension of a group via infinite direct product

Published on 15 Apr 2026 - 9:20

score 64 · Answer 6 · 2026-04-13 04:21:05

64

Views

Question 6 Section Finite Fields Hungerford Algebra

Published on 13 Apr 2026 - 4:21

score 280 · Answer 7 · 2026-04-16 13:59:05

280

Views

A question based on a n irreducible polynomial dividing $x^{q^n}-x$ in finite fields

Published on 16 Apr 2026 - 13:59

score 406 · Answer 8 · 2026-04-15 11:52:05

406

Views

Proving that polynomial f must be of this form if the polynomial is given to be separable

Published on 15 Apr 2026 - 11:52

score 260 · Answer 9 · 2026-04-13 21:19:47

260

Views

Primitive roots of a finite field

Published on 13 Apr 2026 - 21:19

score 144 · Answer 10 · 2026-04-16 07:19:58

144

Views

I need an example of the use of Euler's Theorem for polynomials

Published on 16 Apr 2026 - 7:19

score 137 · Answer 11 · 2026-04-15 03:14:27

137

Views

Squaring is linear in a field of characteristic 2

Published on 15 Apr 2026 - 3:14

score 62 · Answer 12 · 2026-04-13 19:59:34

62

Views

If $f$ is not injective then $F$ is finite.

Published on 13 Apr 2026 - 19:59

score 65 · Answer 13 · 2026-04-17 15:30:21

65

Views

How many morphism $\mathbb{F}_q\to \mathbb{F}_{q^n}$

Published on 17 Apr 2026 - 15:30

score 167 · Answer 14 · 2026-04-17 05:36:50

167

Views

Find the field that $\mathbb{Z}_7[x,y]/\langle y-2x^2, 4xy + y +1 \rangle$ is isomorphic to

Published on 17 Apr 2026 - 5:36

score 43 · Answer 15 · 2026-04-08 22:12:43

43

Views

How to calculate with $\mathbb{Z}/2\mathbb{Z}$ with an unknown variable?

Published on 08 Apr 2026 - 22:12

List Question

Let $K \subset L$ be a finite extension with $p = \text{char}(K) > 0.$ Prove $[L : K]_s \cdot p^k= [L : K]$ for $k \in \mathbb{Z}_{\geq 0}$.

Matrices over $\mathbb{F}_p$ satisfying a Determinant and Trace Condition

Let $p(x)$ be polynomial over $GF(2)$ with $deg(p(x))=8$, show that $g(x)\nmid x^{31}-1$

"smallest" irreducible polynomial over GF(p)

Cohomological dimension of a group via infinite direct product

Question 6 Section Finite Fields Hungerford Algebra

A question based on a n irreducible polynomial dividing $x^{q^n}-x$ in finite fields

Proving that polynomial f must be of this form if the polynomial is given to be separable

Primitive roots of a finite field

I need an example of the use of Euler's Theorem for polynomials

Squaring is linear in a field of characteristic 2

If $f$ is not injective then $F$ is finite.

How many morphism $\mathbb{F}_q\to \mathbb{F}_{q^n}$

Find the field that $\mathbb{Z}_7[x,y]/\langle y-2x^2, 4xy + y +1 \rangle$ is isomorphic to

How to calculate with $\mathbb{Z}/2\mathbb{Z}$ with an unknown variable?

Trending Questions

Popular # Hahtags

Popular Questions