×

zbMATH — the first resource for mathematics

Two exercises concerning the degree of the product of algebraic numbers. (English) Zbl 1220.11131
Summary: Let \(k\) be a field, and let \(\alpha\) and \(\beta\) be two algebraic numbers over \(k\) of degree \(d\) and \(\ell\), respectively. We find necessary and sufficient conditions under which \(\deg(\alpha\beta)=d\ell\) and \(\deg(\alpha+\beta)=d\ell\). Since these conditions are quite difficult to check, we also state a simple sufficient condition for such equalities to occur.

MSC:
11R04 Algebraic numbers; rings of algebraic integers
11R32 Galois theory
12E99 General field theory
PDF BibTeX XML Cite
Full Text: DOI EMIS