Question

If $x_1,\dots,x_n$ purely inseparable and linearly independent over $K$, then they are linearly independent over a separable extension $E$ of $K$.

score 192 · Answer 1 · 2026-04-15 20:15:44

192

Views

If $x_1,\dots,x_n$ purely inseparable and linearly independent over $K$, then they are linearly independent over a separable extension $E$ of $K$.

Published on 15 Apr 2026 - 20:15

score 541 · Answer 2 · 2026-04-14 08:24:47

541

Views

Decomposition of a polynomial in a field extension

Published on 14 Apr 2026 - 8:24

score 87 · Answer 3 · 2026-04-13 22:53:13

87

Views

determine minimal polynomial

Published on 13 Apr 2026 - 22:53

score 94 · Answer 4 · 2026-04-11 19:00:52

94

Views

What is the significance of having a common field extension to prove that any isomorphism sends roots to roots of a polynomial?

Published on 11 Apr 2026 - 19:00

score 320 · Answer 5 · 2026-04-16 03:37:52

320

Views

The Ring extension isomorphic to the field extension

Published on 16 Apr 2026 - 3:37

score 42 · Answer 6 · 2026-04-14 08:42:41

42

Views

structure of extension by quadratic elements

Published on 14 Apr 2026 - 8:42

score 146 · Answer 7 · 2026-04-15 16:28:59

146

Views

Find the intermediate fields of the extension

Published on 15 Apr 2026 - 16:28

score 80 · Answer 8 · 2026-03-29 17:27:02

80

Views

Factor $f(x) = x^4+x^2+x+1$ over $F_2$ by using the Berlekamp's algorithm.

Published on 29 Mar 2026 - 17:27

score 1k · Answer 9 · 2026-04-10 16:22:39

1k

Views

Field extension of odd degree whose Galois group is trivial

Published on 10 Apr 2026 - 16:22

score 366 · Answer 10 · 2026-04-12 21:27:39

366

Views

Finding a transcendence basis of a field over a rational function field in positive characteristic

Published on 12 Apr 2026 - 21:27

score 657 · Answer 11 · 2026-04-10 01:04:54

657

Views

Algebraic Combinations : Meaning

Published on 10 Apr 2026 - 1:04

score 73 · Answer 12 · 2026-04-12 13:40:03

73

Views

simple algebraic extensions with the same minimal polynomial

Published on 12 Apr 2026 - 13:40

score 74 · Answer 13 · 2026-04-10 07:55:33

74

Views

definition of isomorphism between field extensions

Published on 10 Apr 2026 - 7:55

score 67 · Answer 14 · 2026-04-11 18:36:46

67

Views

definition of an isomorphism between field extensions

Published on 11 Apr 2026 - 18:36

score 131 · Answer 15 · 2026-04-15 18:41:50

131

Views

On the restriction of field homomorphisms to subfields

Published on 15 Apr 2026 - 18:41

List Question

If $x_1,\dots,x_n$ purely inseparable and linearly independent over $K$, then they are linearly independent over a separable extension $E$ of $K$.

Decomposition of a polynomial in a field extension

determine minimal polynomial

What is the significance of having a common field extension to prove that any isomorphism sends roots to roots of a polynomial?

The Ring extension isomorphic to the field extension

structure of extension by quadratic elements

Find the intermediate fields of the extension

Factor $f(x) = x^4+x^2+x+1$ over $F_2$ by using the Berlekamp's algorithm.

Field extension of odd degree whose Galois group is trivial

Finding a transcendence basis of a field over a rational function field in positive characteristic

Algebraic Combinations : Meaning

simple algebraic extensions with the same minimal polynomial

definition of isomorphism between field extensions

definition of an isomorphism between field extensions

On the restriction of field homomorphisms to subfields

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