## Variations on the theme of Hilbert’s theorem 90.(English)Zbl 1112.11308

Summary: Given a number field $$K$$, we find two simple separate necessary and sufficient conditions on a given algebraic number for it to be expressible as a quotient (respectively as a difference) of two algebraic numbers conjugate over $$K$$.

### MSC:

 11R04 Algebraic numbers; rings of algebraic integers 11R32 Galois theory
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