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15
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Extension Fields, complex numbers.

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#complex-numbers #field-theory #extension-field
183
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Given a field extension $K\colon F$, $K$ is an $F$-vector space

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#vector-spaces #field-theory #terminology #definition
151
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How cannot localization of any integral domain respect to maximal ideal not be integrally closed?

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#abstract-algebra #ring-theory #commutative-algebra #field-theory #localization
224
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Galois-theory - a question about the galois group

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#abstract-algebra #field-theory #galois-theory #extension-field
1k
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Mistake in proof that a polynomial $f$ irreducible in $F$ is irreducible in $E$ if $\gcd(\deg f, [E:F])=1$

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#abstract-algebra #field-theory #extension-field
226
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pth root of a prime is not in $\mathbb{Q}[\zeta_p,\sqrt[p]{5}]$

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#abstract-algebra #field-theory #galois-theory
307
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Do minimum polynomials always have a nonzero discriminant?

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#abstract-algebra #field-theory #minimal-polynomials
1.7k
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The Kahler differential is zero

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#field-theory #extension-field #universal-property
524
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Writing elements of field extension in terms of the basis determined by a root of a polynomial

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#abstract-algebra #field-theory #extension-field
86
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Subfield generated by a multiplicative subgroup of the field

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#abstract-algebra #field-theory
1.1k
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Field homomorphisms of $\mathbb{R}$

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#abstract-algebra #field-theory
514
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Roots of unity in splitting field of all polynomials of given degree

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#abstract-algebra #field-theory #galois-theory #extension-field
40
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What is the Frobenius element (if any) of this group.

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#group-theory #field-theory
393
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Galois theory with the extension $\mathbb Q(\alpha)/\mathbb Q$

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#abstract-algebra #field-theory #galois-theory #extension-field #splitting-field
13.2k
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How do you show that the degree of an irreducible polynomial over the reals is either one or two?

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#polynomials #field-theory #irreducible-polynomials

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