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Extension-field
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Smallest subfield containing $F$ and $\alpha$
August 1st, 2022
abstract-algebra
extension-field
field-theory
If $a,b\in K$ are algebraic over $k$, then $a\pm b, ab$ and $ab^{-1}$ are also algebraic.
December 21st, 2020
field-theory
extension-field
Determining automorphisms of this extension
August 1st, 2022
extension-field
field-theory
abstract-algebra
galois-theory
How is the prime field "generated"?
October 6th, 2020
extension-field
field-theory
abstract-algebra
Find the degree of the splitting field of $x^6+1$ over $\mathbb{Q}$
August 1st, 2022
field-theory
extension-field
polynomials
abstract-algebra
Conjugate isomorphism of the automorphism groups of two field extensions?
August 1st, 2022
abstract-algebra
extension-field
field-theory
Finding the minimal polynomial in this field extension of $\mathbb Q$?
May 11th, 2020
extension-field
field-theory
polynomials
minimal-polynomials
Prove a Galois group is cyclic
August 1st, 2022
galois-theory
extension-field
abstract-algebra
Compositum of separable extension
August 1st, 2022
extension-field
galois-theory
Prove subset of Field is a subfield
March 17th, 2020
abstract-algebra
field-theory
extension-field
Tower Law and normal field extensions
August 1st, 2022
extension-field
galois-theory
abstract-algebra
Field extension with transcendental number
November 26th, 2020
abstract-algebra
extension-field
Is C the only extension of R with degree 2?
August 1st, 2022
extension-field
abstract-algebra
If the degree of field extension is a prime number, the extension is simple
August 22nd, 2020
extension-field
abstract-algebra
field-theory
Fraleigh's proof of Kronecker's Theorem
May 9th, 2020
extension-field
abstract-algebra
Field extension with odd degree
March 28th, 2020
extension-field
field-theory
abstract-algebra
The degree of the field extension $\mathbb{Q}(\sqrt{5},w): \mathbb{Q}$
August 1st, 2022
finite-fields
galois-theory
extension-field
abstract-algebra
Normal extensions imply that intermediate extensions are normal
August 1st, 2022
extension-field
abstract-algebra
$\mathbb{Q}(\sqrt{m}, \sqrt{n})$ : ring of integers, integral basis and discriminant
October 2nd, 2020
extension-field
ring-theory
field-theory
algebraic-number-theory
Is Q(4th root(2))/Q a galois extension
November 12th, 2020
extension-field
field-theory
galois-theory
Splitting Field of Cubic Polynomial Over the Rationals
August 1st, 2022
abstract-algebra
field-theory
extension-field
splitting-field
Galois group of a polynomial and subfields
August 1st, 2022
extension-field
abstract-algebra
field-theory
galois-theory
The union of finite field extensions is a finite field extension
November 27th, 2020
irreducible-polynomials
abstract-algebra
field-theory
extension-field
Prove that every finite extension field of $\Bbb R$ is either $\Bbb R$ itself or isomorphic to $\Bbb C$.
August 1st, 2022
extension-field
field-theory
If $F$ is a subfield of an algebraically closed field $K$, then the algebraic closure $\overline{F}$ of $F$ in $K$ is also algebraically closed.
August 1st, 2022
irreducible-polynomials
abstract-algebra
field-theory
extension-field
$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
August 1st, 2022
extension-field
galois-theory
Field of algebraic numbers over $\mathbb{Q}$
April 17th, 2022
extension-field
abstract-algebra
field-theory
Subring of a field extension is a subfield
December 12th, 2020
abstract-algebra
extension-field
I need help understanding a proof (Kronecker's theorem)
June 13th, 2020
proof-explanation
field-theory
extension-field
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
August 1st, 2022
extension-field
cyclotomic-fields
galois-theory
field-theory
roots-of-unity
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