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15
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What are $\bar{\mathbb{Q}}$ and $\bar{\mathbb{Q}_{\ell}}$?

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#number-theory #field-theory
298
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The fixed field of a galois group if the characteristic is $p$.

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#field-theory #galois-theory
118
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Separable field extensions

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#abstract-algebra #field-theory #extension-field
214
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finite field extension problem

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#abstract-algebra #polynomials #field-theory #extension-field
1.1k
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Constructing splitting fields

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#abstract-algebra #field-theory #splitting-field
3.4k
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Question About Notation In Field Theory $F(x)$ vs. $F[x]$

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#abstract-algebra #field-theory #notation
636
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Reducibility of a Cyclotomic Polynomial under the ring homomorphism $\mathbb{Z} \rightarrow \mathbb{F}_p$

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#polynomials #ring-theory #field-theory #galois-theory #irreducible-polynomials
3.2k
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If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed?

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#abstract-algebra #field-theory
417
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Is the residue field of an algebraically closed field with respect to a non-trivial valuation infinite?

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#commutative-algebra #field-theory #valuation-theory #tropical-geometry
185
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Does $x\cdot 0 = 0$ follow from the field axioms alone?

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#field-theory #axioms
68
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Tower rule for transcedence degree

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#abstract-algebra #field-theory #extension-field
14
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Why can an ideal generated by a subset be written in this form?

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#ring-theory #field-theory
3.7k
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Proving that the algebraic reals form an infinite field extension over $\mathbb Q$

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#abstract-algebra #field-theory
154
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Galois group of intermediate fields

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#abstract-algebra #group-theory #field-theory #galois-theory
360
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Can't find intermediate subfield of these cyclotomic extensions!

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#field-theory #galois-theory

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