List questions from field-theory

Published on 15 Sep 2014 - 3:01

117

Views

Rational function in both $k(X)[Y]$ and $k(Y)[X]$

Published on 13 Apr 2026 - 5:23

94

Views

Is the map an automorphism?

Published on 12 Apr 2026 - 10:45

86

Views

When people say, "K is an extension of k with dimension n", do they mean as an algebra or as a vectorspace?

Published on 02 Apr 2026 - 12:30

299

Views

Question on the Closure Properties of $\mathbb C$

Published on 12 Apr 2026 - 17:58

85

Views

Number Systems: Determining when they have closure, identities, inverses, and more.

Published on 27 Mar 2026 - 7:49

85

Views

Is the embedding problem with a cyclic kernel always solvable?

Published on 09 Apr 2026 - 13:13

1k

Views

Field Proofs with Multiplicative Inverses

Published on 11 Apr 2026 - 4:04

2.8k

Views

dimension of $\mathbb{Q}(\sqrt2)$

Published on 04 Apr 2026 - 7:22

306

Views

Is $\mathbb{Q}(\sqrt [n]{3})/\mathbb{Q}$ a splitting field of some polynomial

Published on 26 Mar 2026 - 6:28

92

Views

Prove $\mathbb{Q}(\sqrt2,\sqrt2i)=\mathbb{Q}(\sqrt2+\sqrt2i)$

Published on 17 Sep 2014 - 22:56

971

Views

What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?

Published on 02 Apr 2026 - 12:27

951

Views

Learning roadmap in Algebra

Published on 11 Apr 2026 - 7:35

1.2k

Views

$\mathbf{Q}[\sqrt 5+\sqrt[3] 2]=\mathbf{Q}[\sqrt 5,\sqrt[3] 2]$?

Published on 02 Apr 2026 - 12:24

183

Views

$[\mathbb{Q}(\sqrt [3] {2}+\sqrt {5}):\mathbb{Q}]$

Published on 02 Apr 2026 - 12:21

List Question

Write Galois group as semidirect-product

Rational function in both $k(X)[Y]$ and $k(Y)[X]$

Is the map an automorphism?

When people say, "K is an extension of k with dimension n", do they mean as an algebra or as a vectorspace?

Question on the Closure Properties of $\mathbb C$

Number Systems: Determining when they have closure, identities, inverses, and more.

Is the embedding problem with a cyclic kernel always solvable?

Field Proofs with Multiplicative Inverses

dimension of $\mathbb{Q}(\sqrt2)$

Is $\mathbb{Q}(\sqrt [n]{3})/\mathbb{Q}$ a splitting field of some polynomial

Prove $\mathbb{Q}(\sqrt2,\sqrt2i)=\mathbb{Q}(\sqrt2+\sqrt2i)$

What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?

Learning roadmap in Algebra

$\mathbf{Q}[\sqrt 5+\sqrt[3] 2]=\mathbf{Q}[\sqrt 5,\sqrt[3] 2]$?

$[\mathbb{Q}(\sqrt [3] {2}+\sqrt {5}):\mathbb{Q}]$

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