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Explicit calculation of the degree of a number field extension

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#field-theory #extension-field
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Finding the degree of a field extension

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#abstract-algebra #extension-field
159
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Show that $\sqrt{7}\notin\mathbb{Q}(\alpha)$, with $\alpha$ a root of $X^7+6X^3+3X+15$

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#abstract-algebra #polynomials #field-theory #extension-field #irreducible-polynomials
39
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Proving that $[k[u]:k[u^l]]=1$ if $(l,[k[u]:k])=1$

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#abstract-algebra #field-theory #extension-field
18.4k
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How to find the degree of a field extension

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#abstract-algebra #field-theory #definition #extension-field
301
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Field notation and degree of extension

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#algebraic-number-theory #extension-field
2.3k
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Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.

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#abstract-algebra #field-theory #extension-field
85
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Expressing a number field in a simpler way

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#number-theory #field-theory #algebraic-number-theory #extension-field
80
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About $K$-embeddings and the pertinence of an element of a finite and separable field extension

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#field-theory #extension-field
474
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Some field extensions with coprime degrees

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#abstract-algebra #field-theory #extension-field
238
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Finding a subfield of $\mathbb R$ such that $e^2$ is of degree five over that subfield.

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#abstract-algebra #field-theory #extension-field
56
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Checking reducibility for polynomial

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#abstract-algebra #extension-field
91
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Algebraic extension of field with characteristic 0

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#abstract-algebra #algebraic-number-theory #extension-field
146
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Valuation rings are conjugate

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#abstract-algebra #commutative-algebra #galois-theory #extension-field #valuation-theory
1.5k
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Cyclotomic fields of finite fields

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

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