Question

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

score 640 · Answer 1 · 2016-01-29 02:09:47

640

Views

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

Published on 29 Jan 2016 - 2:09

score 89 · Answer 2 · 2026-03-28 05:22:15

89

Views

Proof of equality of $2$ polynomials without using Galois Theory?

Published on 28 Mar 2026 - 5:22

score 1k · Answer 3 · 2016-01-29 19:45:44

1k

Views

Algebraic extension of perfect field in which every polynomial has a root is algebraically closed

Published on 29 Jan 2016 - 19:45

score 121 · Answer 4 · 2026-04-06 11:55:25

121

Views

Simplifying Rational Expressions in a Finite Field Extension

Published on 06 Apr 2026 - 11:55

score 752 · Answer 5 · 2016-01-31 16:16:46

752

Views

Characterizing algebraic extensions

Published on 31 Jan 2016 - 16:16

score 144 · Answer 6 · 2026-03-31 10:34:52

144

Views

Abstract regular curve over non-algebraically closed field

Published on 31 Mar 2026 - 10:34

score 7.2k · Answer 7 · 2016-02-08 16:15:40

7.2k

Views

A field extension of degree 2 is a Normal Extension.

Published on 08 Feb 2016 - 16:15

score 422 · Answer 8 · 2016-02-10 00:46:06

422

Views

Find the fixed field of the following subgroup?

Published on 10 Feb 2016 - 0:46

score 457 · Answer 9 · 2016-02-10 02:43:05

457

Views

Adjoining a separable element to a field makes the extension separable

Published on 10 Feb 2016 - 2:43

score 5.4k · Answer 10 · 2026-04-11 14:52:00

5.4k

Views

To find a field with $p^{2}$ elements, where $p$ is prime

Published on 11 Apr 2026 - 14:52

score 2.3k · Answer 11 · 2026-04-13 16:48:29

2.3k

Views

Product of two transcendental numbers is transcendental

Published on 13 Apr 2026 - 16:48

score 29 · Answer 12 · 2016-02-11 10:41:14

29

Views

What are all the Algebraic Elements of $F(t)$ over $F$?

Published on 11 Feb 2016 - 10:41

score 294 · Answer 13 · 2016-02-11 16:30:22

294

Views

Galois group isomorphic to $\mathbb Z$

Published on 11 Feb 2016 - 16:30

score 1.3k · Answer 14 · 2016-02-11 18:31:11

1.3k

Views

Abelianization of the absolute group and maximal abelian extension

Published on 11 Feb 2016 - 18:31

score 415 · Answer 15 · 2016-02-13 23:50:35

415

Views

Can we extend the real numbers by using hexagonal coordinates on a plane?

Published on 13 Feb 2016 - 23:50

List Question

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

Proof of equality of $2$ polynomials without using Galois Theory?

Algebraic extension of perfect field in which every polynomial has a root is algebraically closed

Simplifying Rational Expressions in a Finite Field Extension

Characterizing algebraic extensions

Abstract regular curve over non-algebraically closed field

A field extension of degree 2 is a Normal Extension.

Find the fixed field of the following subgroup?

Adjoining a separable element to a field makes the extension separable

To find a field with $p^{2}$ elements, where $p$ is prime

Product of two transcendental numbers is transcendental

What are all the Algebraic Elements of $F(t)$ over $F$?

Galois group isomorphic to $\mathbb Z$

Abelianization of the absolute group and maximal abelian extension

Can we extend the real numbers by using hexagonal coordinates on a plane?

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