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If $K/k$ is a finite Galois extension with a galois abelian group, and $ L/k$ any field extension

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
65
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Factorization of prime ideals in Galois closure

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#algebraic-number-theory #maximal-and-prime-ideals #galois-extensions
46
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Degree of Galois extension $F/\mathbb{Q}$ of the splitting field $F$ of $f = X^4 - 20X^2 + 98$

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#abstract-algebra #galois-theory #galois-extensions
140
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Galois group of the Splitting field of $x^4-11$

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#galois-theory #galois-extensions
136
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Finding all the intermediate subfields

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
94
Views

Explicit description connecting homomorphism in Galois cohomology

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#group-cohomology #galois-extensions #galois-cohomology
460
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Finding intermediate subfields of an extension

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#abstract-algebra #galois-theory #extension-field #galois-extensions
145
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Maximal subfields of a commutative algebra

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#abstract-algebra #commutative-algebra #galois-theory #galois-extensions #separable-extension
68
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Galois Groups vs $\mathbb{Q}(\alpha_i)$

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#galois-theory #galois-extensions #group-extensions
911
Views

Quadratic subfield of $\mathbb{Q}(\zeta)$

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#galois-theory #algebraic-number-theory #roots-of-unity #galois-extensions
628
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Field extension $\mathbb{Q}_p(\zeta_{p^n})/\mathbb{Q}_p$ Galois & totally ramified

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#galois-theory #algebraic-number-theory #galois-extensions #local-field
64
Views

Is every $\tau \in \text {Gal} \left (M|K \right ) = \sigma|_M$ for some $\sigma \in \text {Gal} \left (L|K \right )$?

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#field-theory #galois-theory #galois-extensions
76
Views

Possible degrees of separable irreducible polynomials

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#polynomials #galois-theory #algebraic-number-theory #galois-extensions #separable-extension
444
Views

Galois group $G_{L/K}$ of unramified extension and its residue fields

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#algebraic-number-theory #extension-field #galois-extensions #local-field
63
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restrictions to the element $b$, such that $b=\sigma (a)$ where $\sigma$ is a generator of the Galois group

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#abstract-algebra #field-theory #galois-theory #galois-extensions #positive-characteristic

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