On the question of the algebraic independence of algebraic powers of algebraic numbers

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1972 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 11, pages 387-392 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Shmelev, A. A.;

doi: 10.1007/bf01093723

On the question of the algebraic independence of algebraic powers of algebraic numbers

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Abstract

We obtain results showing that transcendental numbers of the form αβ, wherea≠0, 1, β is irrational, anda and β are algebraic numbers, cannot be expressed algebraically in terms of two of the numbers. The proof is carried out by A. O. Gel'fond's method.

Related Organizations

Lomonosov Moscow State University
Russian Federation

Keywords

Transcendence (general theory), Algebraic numbers; rings of algebraic integers

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