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Galois group is $S_{n}$

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#field-theory #galois-theory
125
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Calculating fixed fields

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#abstract-algebra #field-theory #galois-theory
1.4k
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Normal field extension implies splitting field

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#field-theory #extension-field
353
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Example of infinite field $(F,+,.)$ such that $(F^*, . )$ is a cyclic group ?

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#vector-spaces #field-theory #cyclic-groups #infinite-groups
2.6k
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Subgroups and corresponding subfields of galois group of $x^6 + x^3 + 1$

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#field-theory #galois-theory #extension-field
1.1k
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Diagonalisable matrices over different fields

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#linear-algebra #matrices #field-theory #diagonalization
1.1k
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The splitting field of $x^4-4$

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#field-theory #splitting-field
861
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How to find the splitting field of $X^4-10X^2+1$?

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#field-theory #splitting-field
205
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quadratic equation modulo some number

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#number-theory #field-theory #inverse #congruences
152
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Showing that a polynomial over subring is reducible

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#abstract-algebra #field-theory
293
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Ruler and compass constructions and fields

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#abstract-algebra #field-theory
317
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Algebraic closure.

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#abstract-algebra #field-theory
70
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Show that $x^3 + 3x^2 + 9x + 3$ and $x^3 + 3x^2 + 3x − 4$ are irreducible in $\mathbb{Z}[x]$

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#ring-theory #field-theory
3.3k
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Is $x^2-2$ irreducible over R and Q?

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#ring-theory #field-theory
262
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Showing two field extensions (of Q) are isomorphic using primitive elements, and why every element is primitive

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#abstract-algebra #field-theory #galois-theory

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