Question

Polynomial of prime degree: being irreducible or having a root!

score 766 · Answer 1 · 2026-04-16 18:45:16

766

Views

Polynomial of prime degree: being irreducible or having a root!

Published on 16 Apr 2026 - 18:45

score 276 · Answer 2 · 2026-04-15 08:42:53

276

Views

Isomorphism for the group of units of the ring of integers of a local field

Published on 15 Apr 2026 - 8:42

score 671 · Answer 3 · 2026-04-16 02:28:05

671

Views

If $F$ is an extension field of the field $K$ such that $[F:K] =1$, then $F=K$

Published on 16 Apr 2026 - 2:28

score 65 · Answer 4 · 2026-04-12 21:25:58

65

Views

Verification of proof that the left distributive property holds on a field of quotients, F

Published on 12 Apr 2026 - 21:25

score 328 · Answer 5 · 2026-04-14 21:30:48

328

Views

Showing a counterexample regarding normal extension

Published on 14 Apr 2026 - 21:30

score 176 · Answer 6 · 2026-04-16 13:23:43

176

Views

What happens with $S_n$ in rings, integral domains and fields?

Published on 16 Apr 2026 - 13:23

score 461 · Answer 7 · 2026-04-12 23:20:21

461

Views

A good introductory book on Ring and Field theory with a view towards Number Theory ?

Published on 12 Apr 2026 - 23:20

score 79 · Answer 8 · 2026-04-10 21:37:24

79

Views

Reducing a sum of products of primitive nth roots

Published on 10 Apr 2026 - 21:37

score 126 · Answer 9 · 2026-04-15 21:25:04

126

Views

Which Galois Field is isomorphic to this extension?

Published on 15 Apr 2026 - 21:25

score 316 · Answer 10 · 2026-04-11 17:27:46

316

Views

Prime subfield equivalent definitions

Published on 11 Apr 2026 - 17:27

score 72 · Answer 11 · 2026-04-16 17:27:08

72

Views

Find the number of integers $r$ such that the polynomial $x^{r}-a$ has a linear factor over $\mathbb{F}_{p^{n}}$

Published on 16 Apr 2026 - 17:27

score 110 · Answer 12 · 2026-04-15 17:54:54

110

Views

If $a$ is a complex number s.t. $a\notin \mathbb R$, then $\mathbb R(a)=\mathbb C$?

Published on 15 Apr 2026 - 17:54

score 418 · Answer 13 · 2026-04-16 09:26:41

418

Views

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?

Published on 16 Apr 2026 - 9:26

score 363 · Answer 14 · 2026-04-13 12:16:27

363

Views

Finite separable field extensions such that $KL/L$ and $K/K\cap L$ have non-isomorphic automorphism groups

Published on 13 Apr 2026 - 12:16

score 134 · Answer 15 · 2026-04-14 19:37:37

134

Views

Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?

Published on 14 Apr 2026 - 19:37

List Question

Polynomial of prime degree: being irreducible or having a root!

Isomorphism for the group of units of the ring of integers of a local field

If $F$ is an extension field of the field $K$ such that $[F:K] =1$, then $F=K$

Verification of proof that the left distributive property holds on a field of quotients, F

Showing a counterexample regarding normal extension

What happens with $S_n$ in rings, integral domains and fields?

A good introductory book on Ring and Field theory with a view towards Number Theory ?

Reducing a sum of products of primitive nth roots

Which Galois Field is isomorphic to this extension?

Prime subfield equivalent definitions

Find the number of integers $r$ such that the polynomial $x^{r}-a$ has a linear factor over $\mathbb{F}_{p^{n}}$

If $a$ is a complex number s.t. $a\notin \mathbb R$, then $\mathbb R(a)=\mathbb C$?

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?

Finite separable field extensions such that $KL/L$ and $K/K\cap L$ have non-isomorphic automorphism groups

Is the formula $[k(a,b):k][k(a) \cap k(b):k] = [k(a):k][k(b):k]$ true for simple algebraic extensions ($k(a)/k$ and $k(b)/k$ )?

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