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If $\alpha$ is an algebraic number, then prove that $\frac{2}{3}\alpha$ is also algebraic.

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#abstract-algebra #algebraic-number-theory #galois-theory
130
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suggestion about elliptic curves

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#algebraic-number-theory
72
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Particular determinant made of powers of algebraic numbers is nonzero?

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#linear-algebra #algebraic-number-theory
1.6k
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Embedding into $p$-adic complex numbers

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#number-theory #algebraic-number-theory #analytic-number-theory #p-adic-number-theory
977
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How to determine the density of the set of completely splitting primes for a finite extension?

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#number-theory #algebraic-number-theory #galois-theory
2.3k
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Cyclotomic Character

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#number-theory #algebraic-number-theory #roots-of-unity #galois-representations
783
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Completion of the unit group of a local field

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#abstract-algebra #algebraic-number-theory #local-field
103
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On number of different factorizations over integers of a number field

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#algebraic-number-theory #factoring
155
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Do conjugate fields have the same maximal order?

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#abstract-algebra #field-theory #algebraic-number-theory
154
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$p$ is an odd prime of the form $p=x^2+2y^2$ iff $p\equiv_8$ $1$ or $3$

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#elementary-number-theory #algebraic-number-theory
274
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Number of field extensions of $\mathbb{Q}_p$

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#algebraic-number-theory #p-adic-number-theory
306
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Formula for Hilbert symbol for primes lying above 2

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#algebraic-number-theory #valuation-theory
81
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Infinite primes and notation

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#number-theory #notation #algebraic-number-theory #rational-numbers
505
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Scalar extension of simple algebras

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#algebraic-number-theory #noncommutative-algebra #algebras
621
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$p$-part of cyclotomic character

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#algebraic-number-theory #galois-theory #p-adic-number-theory

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