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Can the norm of a non-algebraic integer be an integer?

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#algebraic-number-theory
258
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Number of algebraic integer divisors of an algebraic integer

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#number-theory #elementary-number-theory #algebraic-number-theory #analytic-number-theory
188
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The number of abolute value on $\mathbb{Q}(\sqrt{2})$

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#abstract-algebra #algebraic-number-theory #valuation-theory
56
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Is $\Bbb{R}$ finitely generated over the algebraics?

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#algebraic-number-theory #extension-field #real-numbers
798
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Specializations of elementary symmetric polynomials

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#combinatorics #algebraic-number-theory #generating-functions #symmetric-polynomials
901
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If $\widetilde{L} =$ splitting field of all irreducible polynomials over $L$ of prime-power degree, is $\widetilde{\Bbb{Q}} = \overline{\Bbb{Q}}$?

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#algebraic-number-theory #galois-theory
1.3k
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On Hilbert Class Polynomial

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#algebraic-number-theory #math-software #class-field-theory #sagemath
779
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Ramification of the prime at infinity of function fields

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#number-theory #algebraic-number-theory #ramification
196
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What is the largest possible length of a prime number?

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#number-theory #elementary-number-theory #algebraic-number-theory
303
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Subgroup of class group

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#algebraic-number-theory #galois-theory
265
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Is the extension Galois if $\mathrm{Aut}(K)$ acts transitively on the non-ramified prime ideals?

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#abstract-algebra #number-theory #field-theory #algebraic-number-theory #galois-theory
224
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Normalisation of $\mathbb{Z}$ in $\mathbb{Q}(\sqrt{d})$ is UFD...

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#abstract-algebra #arithmetic #algebraic-number-theory
193
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When is a number in $\mathbb{Q}(\sqrt{a_1},\ldots,\sqrt{a_n})$?

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#algorithms #algebraic-number-theory #galois-theory #minimal-polynomials #splitting-field
860
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Dedekind's criterion clarification

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#algebraic-number-theory #ideals #dedekind-domain
203
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$\zeta$ primitive $n$th root of unity, help showing that $\sqrt{n},\sqrt{-n}\in \mathbb{Q}(\zeta)$ under some conditions.

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#algebraic-number-theory #cyclotomic-polynomials

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