Question

How to show $\sqrt[3]{X-i}\notin \mathbb{C}(X,\sqrt[3]{X+i})$

score 63 · Answer 1 · 2014-07-18 16:02:10

63

Views

How to show $\sqrt[3]{X-i}\notin \mathbb{C}(X,\sqrt[3]{X+i})$

Published on 18 Jul 2014 - 16:02

score 213 · Answer 2 · 2014-07-19 14:27:14

213

Views

prove that if $p(x)\in R[x]$ is reducible over $F[x]$ then $p(x)$ is reducible over $R[x]$.

Published on 19 Jul 2014 - 14:27

score 64 · Answer 3 · 2014-07-20 02:24:50

64

Views

How to show the cyclotomic polynomial is irreducible over $\mathbb{R}(T,\sqrt[n]{T})$

Published on 20 Jul 2014 - 2:24

score 272 · Answer 4 · 2026-04-12 18:46:09

272

Views

Existence of Irreducible polynomials over Z of any given degree which do not satisfy the Eisenstein's Criterion

Published on 12 Apr 2026 - 18:46

score 359 · Answer 5 · 2026-04-12 04:34:29

359

Views

Proof that all ordered fields are in the Surreals

Published on 12 Apr 2026 - 4:34

score 349 · Answer 6 · 2026-04-10 18:38:09

349

Views

The lattice of closed subsets of an algebraic closure operator is an algebraic lattice

Published on 10 Apr 2026 - 18:38

score 46 · Answer 7 · 2026-04-12 08:45:01

46

Views

Is a finitely generated extension of a real closed field also real closed?

Published on 12 Apr 2026 - 8:45

score 114 · Answer 8 · 2014-07-24 01:47:56

114

Views

For extension fields, does $[F(a,b):F(a)]=[F(b):F]$?

Published on 24 Jul 2014 - 1:47

score 113 · Answer 9 · 2014-07-24 04:09:42

113

Views

How do we know that $\mathbb{Q}$ is the initial field of characteristic $0$?

Published on 24 Jul 2014 - 4:09

score 256 · Answer 10 · 2026-03-30 00:20:16

256

Views

Find a multiplicative inverse of an element in a field

Published on 30 Mar 2026 - 0:20

score 786 · Answer 11 · 2026-04-11 00:14:52

786

Views

A question about algebraically closed fields

Published on 11 Apr 2026 - 0:14

score 285 · Answer 12 · 2026-04-11 20:39:19

285

Views

Is there any subset of Complex numbers that is algebraically closed?

Published on 11 Apr 2026 - 20:39

score 2.3k · Answer 13 · 2026-04-02 03:49:19

2.3k

Views

$F/K$ algebraic and every nonconstant polynomial in $K[X]$ has a root in $F$ implies $F$ is algebraically closed.

Published on 02 Apr 2026 - 3:49

score 63 · Answer 14 · 2026-04-04 00:51:13

63

Views

$K \le B\le F$, If $F$ Galois over $K$ $\Rightarrow$ $F$ a Galois over $B$

Published on 04 Apr 2026 - 0:51

score 664 · Answer 15 · 2026-04-11 11:53:05

664

Views

A finite commutative ring with 1 whose elements satisfy a particular equation

Published on 11 Apr 2026 - 11:53

List Question

How to show $\sqrt[3]{X-i}\notin \mathbb{C}(X,\sqrt[3]{X+i})$

prove that if $p(x)\in R[x]$ is reducible over $F[x]$ then $p(x)$ is reducible over $R[x]$.

How to show the cyclotomic polynomial is irreducible over $\mathbb{R}(T,\sqrt[n]{T})$

Existence of Irreducible polynomials over Z of any given degree which do not satisfy the Eisenstein's Criterion

Proof that all ordered fields are in the Surreals

The lattice of closed subsets of an algebraic closure operator is an algebraic lattice

Is a finitely generated extension of a real closed field also real closed?

For extension fields, does $[F(a,b):F(a)]=[F(b):F]$?

How do we know that $\mathbb{Q}$ is the initial field of characteristic $0$?

Find a multiplicative inverse of an element in a field

A question about algebraically closed fields

Is there any subset of Complex numbers that is algebraically closed?

$F/K$ algebraic and every nonconstant polynomial in $K[X]$ has a root in $F$ implies $F$ is algebraically closed.

$K \le B\le F$, If $F$ Galois over $K$ $\Rightarrow$ $F$ a Galois over $B$

A finite commutative ring with 1 whose elements satisfy a particular equation

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