PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)Vol. 77(91), pp. 67–70 (2005)
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PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 77(91), pp. 67–70 (2005) |
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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.
© 2005 Mathematical Institute of the Serbian Academy of Science and Arts
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