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Determining the Galois Group of Splitting Field of Cubic polynomials

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#abstract-algebra #field-theory #galois-theory
66
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Field extensions confusion

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#abstract-algebra #field-theory #galois-theory #extension-field
242
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Extending Isomorphisms

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#field-theory #galois-theory #extension-field #ring-isomorphism
1.4k
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Is every primitive element of a finite field of characteristic $2$, a generator of the multiplicative group?

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#abstract-algebra #group-theory #field-theory #galois-theory #finite-fields
192
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The function field of a modular curve

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#galois-theory #riemann-surfaces
98
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The degree of a field extension

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#field-theory #galois-theory
273
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Why are all Frobenius elements conjugated?

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#group-theory #galois-theory #algebraic-number-theory #local-field #galois-representations
84
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General findings about Galois groups

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#polynomials #galois-theory #big-list
744
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Symmetries of polynomials

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#polynomials #galois-theory #symmetry
98
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The function $G:\mathbb{Q}^n \rightarrow \mathsf{FinGroup}$

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#polynomials #galois-theory
66
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"smallest" field where a polynomial is reducible

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#commutative-algebra #field-theory #galois-theory #extension-field
190
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Can Abel-Ruffini be "seen" by looking at the graphs of polynomials?

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#abstract-algebra #polynomials #galois-theory #roots
99
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Showing $\sum_{i=1}^nq_i\sqrt{p_i}+q_0$ is irrational for $q_0,...,q_n\in\mathbb{Q}$, $q_1,...,q_n\not=0$, and $p_i$ distinct prime

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#abstract-algebra #analysis #galois-theory #roots #irrational-numbers
1.1k
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Show a regular n-sided polygon is constructible, using only ruler and compasses, iff the number $\alpha = 2 \cos(2\pi/n)$ is constructible.

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#proof-writing #galois-theory #extension-field #geometric-construction #galois-extensions
44
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How to prove isomorphism for rings in Galois Theory?

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#galois-theory #ideals #ring-isomorphism

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