PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 77(91), pp. 67–70 (2005) 

TWO EXERCISES CONCERNING THE DEGREE OF THE PRODUCT OF ALGEBRAIC NUMBERSArturas DubickasDepartment of Mathematics and Informatics, Vilnius University, Vilnius, LithuaniaAbstract: 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. Keywords: field, algebraic number, degree, root of unity Classification (MSC2000): 11R04; 11R32, 12E99 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 7 Nov 2005. This page was last modified: 11 May 2006.
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