Question

Why is the subfield (of a field) generated by an algebraic element equal to the subring generated by the same element?

score 854 · Answer 1 · 2014-07-05 10:22:02

854

Views

Why is the subfield (of a field) generated by an algebraic element equal to the subring generated by the same element?

Published on 05 Jul 2014 - 10:22

score 75 · Answer 2 · 2014-07-05 12:30:06

75

Views

Is $\mathbb{Q}[X]/(X^2+1) \cong \mathbb{Q}[X]/(X^2-1)$

Published on 05 Jul 2014 - 12:30

score 134 · Answer 3 · 2026-04-03 23:05:00

134

Views

If $L_1/K$ and $L_2/K$ are not Galois (solvable), then $L_1L_2/K$ is not Galois (solvable)

Published on 03 Apr 2026 - 23:05

score 58 · Answer 4 · 2026-04-11 23:53:01

58

Views

Possible Fields?

Published on 11 Apr 2026 - 23:53

score 187 · Answer 5 · 2026-04-12 04:37:13

187

Views

Euclid and finite fields

Published on 12 Apr 2026 - 4:37

score 74 · Answer 6 · 2014-07-07 21:24:13

74

Views

what is this property called?(Field theory)

Published on 07 Jul 2014 - 21:24

score 275 · Answer 7 · 2026-04-11 17:51:47

275

Views

Is there a universal property in this proposition (which regards field extensions)?

Published on 11 Apr 2026 - 17:51

score 71 · Answer 8 · 2026-04-04 00:54:16

71

Views

Proving that a certain maximal subfield has countably infinite index

Published on 04 Apr 2026 - 0:54

score 841 · Answer 9 · 2026-04-04 00:44:05

841

Views

Prove that $k(\alpha+\beta)=k(\alpha,\beta)$

Published on 04 Apr 2026 - 0:44

score 167 · Answer 10 · 2026-04-11 00:15:18

167

Views

A question about separable extension

Published on 11 Apr 2026 - 0:15

score 598 · Answer 11 · 2014-07-10 04:30:09

598

Views

Does there exist two non-constant polynomials $f(x),g(x)\in\mathbb Z[x]$ such that for all integers $m,n$, gcd$(f(m),g(n))=1$?

Published on 10 Jul 2014 - 4:30

score 3.8k · Answer 12 · 2026-04-11 03:42:51

3.8k

Views

What is the meaning of "fix" in field theory?

Published on 11 Apr 2026 - 3:42

score 75 · Answer 13 · 2026-04-04 00:44:05

75

Views

$(u+1)(u+2)\cdots(u+p)=u^p-u$

Published on 04 Apr 2026 - 0:44

score 1.3k · Answer 14 · 2026-04-09 23:08:34

1.3k

Views

What is the difference between field theory and Galois theory

Published on 09 Apr 2026 - 23:08

score 806 · Answer 15 · 2026-04-12 14:27:29

806

Views

Radical Solvable quintic polynomial.

Published on 12 Apr 2026 - 14:27

List Question

Why is the subfield (of a field) generated by an algebraic element equal to the subring generated by the same element?

Is $\mathbb{Q}[X]/(X^2+1) \cong \mathbb{Q}[X]/(X^2-1)$

If $L_1/K$ and $L_2/K$ are not Galois (solvable), then $L_1L_2/K$ is not Galois (solvable)

Possible Fields?

Euclid and finite fields

what is this property called?(Field theory)

Is there a universal property in this proposition (which regards field extensions)?

Proving that a certain maximal subfield has countably infinite index

Prove that $k(\alpha+\beta)=k(\alpha,\beta)$

A question about separable extension

Does there exist two non-constant polynomials $f(x),g(x)\in\mathbb Z[x]$ such that for all integers $m,n$, gcd$(f(m),g(n))=1$?

What is the meaning of "fix" in field theory?

$(u+1)(u+2)\cdots(u+p)=u^p-u$

What is the difference between field theory and Galois theory

Radical Solvable quintic polynomial.

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