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15
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Prove that M is an extension of N of degree 2

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#field-theory #galois-theory #galois-extensions
71
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Galois group of the polynomial $f(X)=(X^4+1)(X^4-2)$

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#field-theory #galois-theory #extension-field #galois-extensions
237
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Splitting field of $8$-th root of the unity is Galois

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#field-theory #galois-theory #splitting-field #galois-extensions #cyclotomic-polynomials
290
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Subfields of galois field

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#abstract-algebra #galois-theory #extension-field #galois-extensions
129
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Show there are elements $x,y\in K$, s.t. $x^2+y^2=-1$

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#field-theory #galois-theory #algebraic-number-theory #galois-extensions
755
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Is Q(4th root(2)):Q(sqrt(2)) a Galois extension?

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#galois-theory #galois-extensions
139
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Profinite groups are Galois groups

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#group-theory #galois-theory #topological-groups #galois-extensions #profinite-groups
42
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confused about Lemma 5.33 (about Galois Theory) in Rotman's textbook

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#abstract-algebra #field-theory #galois-theory #galois-extensions
196
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Galois group of an irreducible polynomial of degree 4 is not cyclic

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#abstract-algebra #galois-theory #splitting-field #galois-extensions
80
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Show $\mathbb{Q}(\sqrt{p}\: |\: p\text{ prime})$ is a normal extension of $\mathbb{Q}$

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#field-theory #galois-theory #extension-field #galois-extensions
99
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Alternative Definition of Galois

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#abstract-algebra #field-theory #solution-verification #galois-theory #galois-extensions
428
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Are there any rigid number fields?

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
495
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Definition of Frobenius automorphism

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#galois-theory #algebraic-number-theory #finite-fields #automorphism-group #galois-extensions
71
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Polynomial division over different fields

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#abstract-algebra #polynomials #irreducible-polynomials #galois-extensions
123
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Upper bound for discriminant of Galois closure

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#algebraic-number-theory #galois-extensions #discriminant

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