Question

Clarification of: $f$ has no multiple root in any field extension of $F$ unless $f'$ is the zero polynomial

score 881 · Answer 1 · 2018-04-18 00:25:11

881

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Clarification of: $f$ has no multiple root in any field extension of $F$ unless $f'$ is the zero polynomial

Published on 18 Apr 2018 - 0:25

score 610 · Answer 2 · 2018-04-18 17:35:30

610

Views

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Published on 18 Apr 2018 - 17:35

score 62 · Answer 3 · 2026-03-22 23:47:56

62

Views

Intermediate Fields and Root Fields

Published on 22 Mar 2026 - 23:47

score 59 · Answer 4 · 2018-04-19 03:40:56

59

Views

How can I show $\sqrt{2-\sqrt{2}} \in \mathbb Q\Big(\sqrt{2+\sqrt{2}}\Big)$?

Published on 19 Apr 2018 - 3:40

score 41 · Answer 5 · 2026-03-25 01:18:55

41

Views

Let $K \prec F$ and $\tau : F \rightarrow$ is a homomorphism where $\tau(u) = u \forall u\in K$ then $\tau \in \text{Gal}_K F$

Published on 25 Mar 2026 - 1:18

score 145 · Answer 6 · 2026-03-25 01:20:31

145

Views

What is connection between Modules and Fields in mathematics ? Is maybe quotient of the action / space of coinvariants?

Published on 25 Mar 2026 - 1:20

score 388 · Answer 7 · 2018-04-20 17:45:23

388

Views

How to show that the two extensions are isomorphic?

Published on 20 Apr 2018 - 17:45

score 152 · Answer 8 · 2018-04-21 23:55:46

152

Views

Find all integers n such that its root is in Q adjoin root 2

Published on 21 Apr 2018 - 23:55

score 292 · Answer 9 · 2018-04-22 19:23:23

292

Views

Question about Galois Extension and fixed field by a Subgroup of the Galois group

Published on 22 Apr 2018 - 19:23

score 102 · Answer 10 · 2018-04-22 21:18:50

102

Views

Irreducible Polynomial $g = X^4 + X + 1$ in $\mathbb{F}_2$

Published on 22 Apr 2018 - 21:18

score 95 · Answer 11 · 2018-04-23 16:57:03

95

Views

Field extensions isomorphic to subfields of each other

Published on 23 Apr 2018 - 16:57

score 62 · Answer 12 · 2018-04-23 20:33:30

62

Views

How to show isomorphism between extension fields?

Published on 23 Apr 2018 - 20:33

score 624 · Answer 13 · 2026-03-25 06:29:37

624

Views

Elementary proof of "irreducible polynomials remain irreducible over transcendental extension"?

Published on 25 Mar 2026 - 6:29

score 64 · Answer 14 · 2018-04-27 12:39:24

64

Views

Every cubic extension $L/K$ is of the shape $L=K(\sqrt[3]{\alpha})$ with $\alpha$ not a cubed number and $\text{char}(K)\neq3$

Published on 27 Apr 2018 - 12:39

score 104 · Answer 15 · 2018-04-27 15:20:34

104

Views

Question about Galois Theory. Extension of a field of odd characteristic.

Published on 27 Apr 2018 - 15:20

List Question

Clarification of: $f$ has no multiple root in any field extension of $F$ unless $f'$ is the zero polynomial

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Intermediate Fields and Root Fields

How can I show $\sqrt{2-\sqrt{2}} \in \mathbb Q\Big(\sqrt{2+\sqrt{2}}\Big)$?

Let $K \prec F$ and $\tau : F \rightarrow$ is a homomorphism where $\tau(u) = u \forall u\in K$ then $\tau \in \text{Gal}_K F$

What is connection between Modules and Fields in mathematics ? Is maybe quotient of the action / space of coinvariants?

How to show that the two extensions are isomorphic?

Find all integers n such that its root is in Q adjoin root 2

Question about Galois Extension and fixed field by a Subgroup of the Galois group

Irreducible Polynomial $g = X^4 + X + 1$ in $\mathbb{F}_2$

Field extensions isomorphic to subfields of each other

How to show isomorphism between extension fields?

Elementary proof of "irreducible polynomials remain irreducible over transcendental extension"?

Every cubic extension $L/K$ is of the shape $L=K(\sqrt[3]{\alpha})$ with $\alpha$ not a cubed number and $\text{char}(K)\neq3$

Question about Galois Theory. Extension of a field of odd characteristic.

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