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15
125
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A basis in $\mathbb{Q}(\pi)$

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#abstract-algebra #extension-field
53
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Dimension of $\mathbb{Q(\omega)}$ and minimal polynomial of $\sqrt[3]{2}$

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#vector-spaces #field-theory #extension-field #irreducible-polynomials #minimal-polynomials
85
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How does the Galois group of a splitting field act on a specific element?

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#abstract-algebra #polynomials #galois-theory #extension-field #splitting-field
94
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If $\mathbb Q[a,b]$ is a field, then are $a$ and $b$ algebraic?

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#abstract-algebra #field-theory #extension-field
88
Views

Help with understanding radical extensions in Galois theory (decomposition field of the polynomial $X^n-a$ over $k$)

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#abstract-algebra #field-theory #galois-theory #finite-fields #extension-field
44
Views

The map $\phi:Gal(KL/L)\to Gal(K/F)$ is well defined

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#field-theory #galois-theory #extension-field
49
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Find the dimension of $\mathbb{Q(\sqrt{5},i)}$ over $\mathbb{Q}$

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#extension-field #minimal-polynomials
47
Views

Is it possible for an incompletely valued field to have a finite-degree extension which is complete?

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#field-theory #extension-field #valuation-theory
96
Views

Degree of a field over intersection

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#abstract-algebra #field-theory #galois-theory #extension-field
160
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A property of constructible elements over $\mathbb{Q}$

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#galois-theory #extension-field
137
Views

Are the split-complex numbers a proper algebraic extension of the real numbers?

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#abstract-algebra #field-theory #extension-field
121
Views

Why the assumption 'L is contained in an algebraic closure of K' is required in the definition of normal extension?

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#abstract-algebra #field-theory #galois-theory #extension-field
102
Views

Conditions for the tower of Galois extensions of local fields to be a Galois extension

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#number-theory #field-theory #galois-theory #extension-field #local-field
50
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Show $\mathbb{F}_p(b)=\mathbb{F}_{p^{pk}}$ where $1/(1-b)$ is a root of $x^p-x-a^{-1}$

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#abstract-algebra #number-theory #finite-fields #extension-field #field-trace
71
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Is field extension T(a,b)=T(a)(b)?

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#abstract-algebra #field-theory #algebraic-number-theory #extension-field

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