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Finding Primitive Elements of Separable Function Field Extensions

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#algebraic-geometry #field-theory #extension-field #algebraic-curves #function-fields
60
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For each polynomial $p \in K[t]$, there exists another polynomial $g$ such that $\{p(\epsilon_i): 1\leq i \leq n\}$ is its set of roots

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#abstract-algebra #galois-theory #extension-field #splitting-field
95
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Simple extension over a field $\mathbb{Q}(\sqrt{7})$

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#extension-field
286
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Show that this polynomial (involving n-th roots of unity) has rational coefficients

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#galois-theory #extension-field
61
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Non-existence of a particular type of tower of number fields

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#abstract-algebra #field-theory #algebraic-number-theory #extension-field
143
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Intermediate field extensions of $\mathbb{Q}(\zeta_3)/\mathbb{Q}$

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#abstract-algebra #field-theory #galois-theory #extension-field
290
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Galois Extension.

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#abstract-algebra #field-theory #galois-theory #extension-field
63
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Galois Group is $\mathbb{Z}/4\mathbb{Z}$.

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#field-theory #galois-theory #extension-field #splitting-field
152
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Splitting field and automorphisms

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#abstract-algebra #ring-theory #field-theory #extension-field #splitting-field
130
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kummer extension on SAGE

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#extension-field #sagemath #kummer-theory
53
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What can we say about the dimension of $[ E : F]$ if $F$ is finite and $f \in F[x]$ min. polynomial

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#abstract-algebra #field-theory #finite-fields #extension-field
684
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Determining the degree of a root of unity over a cyclotomic expansion

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#abstract-algebra #extension-field #cyclotomic-polynomials
1.9k
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Galois Theory.Subgroups of Galois Group

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#finite-groups #galois-theory #extension-field
209
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Normal extension of a field

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#abstract-algebra #field-theory #examples-counterexamples #extension-field
107
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Zeros of specialization of a family of polynomials

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#abstract-algebra #algebraic-geometry #commutative-algebra #field-theory #extension-field

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