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15
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Some questions about sub-fields of the field of complex numbers

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#number-theory #field-theory
302
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Counting the roots of a polynomial over a finite field

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#field-theory #finite-fields #extension-field #roots-of-unity #splitting-field
96
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Presence of non square elements in $GF(p)$

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#abstract-algebra #field-theory #finite-fields #extension-field
1.1k
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Proving that either $x $ or $2x$ is a generator of the cyclic group $(\mathbb Z_3[x]/\langle f(x) \rangle)^*$

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#abstract-algebra #field-theory #finite-fields
2.5k
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What would be a prime element in the field of rational numbers?

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#abstract-algebra #ring-theory #field-theory
66
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Field of prime characteristic over two indeterminates

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#abstract-algebra #field-theory #positive-characteristic
90
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Splitting field of $(x^2-2)(x^6-20)$ over $\mathbb{Q}$

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#abstract-algebra #field-theory #splitting-field
133
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If the field has prime field isomorphic to $\mathbb{Q}$ would there be any subfield isomorphic to $\mathbb{Q}$?

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#field-theory
3.6k
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Minimal polynomial and field extension

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#abstract-algebra #field-theory #extension-field #minimal-polynomials
99
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Irreducible polynomial

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#abstract-algebra #polynomials #field-theory #irreducible-polynomials
1.2k
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What is the relationship between the trace/norm of a quaternion and the definition in field theory?

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#abstract-algebra #vector-spaces #field-theory #algebraic-number-theory #extension-field
134
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An infinite extension of $\mathbb Q$

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#field-theory
103
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Field extensions: compute the degree of an extension.

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#abstract-algebra #field-theory #extension-field
564
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Finding a cubic polynomial whose splitting field over $\mathbb{Q}$ equals $\mathbb{Q}(a)$ if $a$ is any of its roots

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#abstract-algebra #number-theory #field-theory #galois-theory
248
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In which Fields, does $x^n-x$ have a multiple zero?

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#abstract-algebra #field-theory

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