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Etale cohomology and restricted direct product

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#algebraic-number-theory #arithmetic-geometry #etale-cohomology
215
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Finding a primitive element for the Hilbert Class Field of $\mathbb{Q}(\sqrt{-14})$

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#abstract-algebra #algebraic-number-theory #galois-theory
190
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Abelian extensions under inclusion, and their conductors

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#algebraic-number-theory #class-field-theory
227
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number theory of coefficients in an infinite sequence of polynomials

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#number-theory #polynomials #algebraic-number-theory #recurrence-relations #quadratic-forms
665
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$\mathbb{Q}(\sqrt[p]{q}) \neq \mathbb{Q}(\sqrt[p]{r})$ for $p,q,r$ primes and $q \neq r$.

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#algebraic-number-theory #galois-theory #extension-field
4k
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Solved Problems in Algebraic Number Theory

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#number-theory #soft-question #algebraic-number-theory
261
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When does coprimality carry over to the base ring in an integral extension of Dedekind domains?

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#commutative-algebra #algebraic-number-theory #ideals #dedekind-domain
206
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Ordering the solutions to Pell's Equation

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#number-theory #elementary-number-theory #algebraic-number-theory
229
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Factorising ideals in $\mathbb{Z}[\sqrt{10}]$

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#algebraic-number-theory
119
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Find extension of $\mathbb{Q}$ containing components of eigenvectors of a matrix

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#number-theory #eigenvalues-eigenvectors #algebraic-number-theory #extension-field
306
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Find primitive element of splitting field of $1 + x + x^2 - x^5$

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#number-theory #field-theory #algebraic-number-theory #splitting-field
275
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Finding a particular integral basis of the cyclotomic field

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#number-theory #algebraic-number-theory
1.7k
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Residue class field of ring of integers is finite

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#algebraic-number-theory
129
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Proposition 17, p. 68 of Lang's Algebraic Number Theory

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#abstract-algebra #number-theory #elementary-number-theory #ring-theory #algebraic-number-theory
55
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If $r$ a primitive root of unity then $\frac{r-1}{r^k- 1}$ is an algebraic integer in $\mathbb Q(r)$

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#algebraic-number-theory #roots-of-unity

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