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Every finite extension of a finite field is Galois

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#galois-theory #finite-fields #extension-field
95
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Galois descent morphism and Galois descent

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#galois-theory
123
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Minimal polynomial in splitting field completion

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#field-theory #galois-theory #algebraic-number-theory #prime-factorization #minimal-polynomials
31
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How many morphism extensions for a simple field extension?

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#field-theory #galois-theory #extension-field
486
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Prove that there exists a non-principal ideal in $Q(\zeta_{23})$.

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#galois-theory #algebraic-number-theory #dedekind-domain #cyclotomic-fields
109
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Inertia group of function field

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#galois-theory #algebraic-number-theory #ramification #function-fields
68
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Proof that the extension is galois

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#galois-theory #algebraic-number-theory
186
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Can we determine the set of all angles that can be trisected

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#galois-theory #extension-field #geometric-construction
73
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Find the minimal polynomial of $\alpha^i$ for $i$, $0 \le \le 48$, over $GF(7)$.

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#abstract-algebra #field-theory #galois-theory
221
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Non cyclic galois extension

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#galois-theory #cyclic-groups #splitting-field
110
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Compute Galois group of extension

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#polynomials #galois-theory #finite-fields #laurent-series
379
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elements with field trace 0 in Galois field extensions

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#galois-theory
122
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proof of some statement about finite field extension

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#galois-theory #finite-fields #cyclic-groups #laurent-series
218
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$\alpha$ is a root of the polynomial $^2++3$ in $GF(49)$. Express every element of $GF(49)^*$

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#abstract-algebra #field-theory #galois-theory
203
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How to factor $^{49}−$ over $GF(7)$ as a product of irreducible polynomials.

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#abstract-algebra #polynomials #galois-theory #irreducible-polynomials

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