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Proving $n^q$ is algebraic when $n\in \mathbb N$ and $q\in \mathbb Q$.

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#real-analysis #algebraic-number-theory
151
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Integral closure as topological closure

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#abstract-algebra #general-topology #algebraic-number-theory
149
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Number fields and algebraic integer

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#field-theory #algebraic-number-theory #extension-field
103
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If a ring has its field of fraction as algebraic number field $K$, would this ring be $O_K$?

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#ring-theory #field-theory #algebraic-number-theory
211
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Unramification of Ideals in Pure Cubic fields

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#algebraic-number-theory #class-field-theory
501
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Infinite primes of a number field

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#abstract-algebra #number-theory #algebraic-number-theory #valuation-theory
355
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Any general "formula" solutions for higher order polynomial equation?

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#abstract-algebra #algebraic-number-theory #galois-theory #diophantine-equations
52
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Orderings of $\mathbb Q[\zeta]$

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#algebraic-number-theory
706
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Abelian Kummer Extension

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#abstract-algebra #algebraic-number-theory #galois-theory
307
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Algebraic number theory book with answers to selected questions for self-study?

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#number-theory #reference-request #algebraic-number-theory #analytic-number-theory #book-recommendation
177
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$\sqrt {-6}$ is not prime in $\mathbb{Z}+\mathbb{Z}\sqrt {-6}$

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#elementary-number-theory #algebraic-number-theory
392
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Decomposition group of a prime ideal and root of polynomials

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#algebraic-number-theory #galois-theory
1.6k
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Show that $\sqrt{-6}$ is irreducible in $\mathbb{Z}+\mathbb{Z}\sqrt{-6}$

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#algebraic-number-theory
144
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Are these proposed rules for the canonical factorization of algebraic integers complete?

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#soft-question #notation #algebraic-number-theory
450
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Does there exist a finite set of polynomials which do not have roots over any prime field?

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#number-theory #polynomials #prime-numbers #algebraic-number-theory #irreducible-polynomials

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