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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Composition of quadratic forms over number fields
 Zemková, Kristýna ; Kala, Vítězslav (advisor) ; Francírek, Pavel (referee)
The thesis is concerned with the theory of binary quadratic forms with coefficients in the ring of algebraic integers of a number field. Under the assumption that the number field is of narrow class number one, there is developed a theory of composition of such quadratic forms. For a given discriminant, the composition is determined by a bijection between classes of quadratic forms and a so-called relative oriented class group (a group closely related to the class group). Furthermore, Bhargava cubes are generalized to cubes with entries from the ring of algebraic integers; by using the composition of quadratic forms, the composition of Bhargava cubes is proved in the generalized case. 1
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Norm-euclidean quadratic extensions of the field of rational numbers
 Zemková, Kristýna ; Šaroch, Jan (advisor) ; Příhoda, Pavel (referee)
The goal of this work is to characterize all norm-euclidean quadratic ex- tensions of Q. The work treats completely the part of imaginary quadratic extensions. In the case of real quadratic extensions, we give a list of such dis- criminants D that the field Q( √ D) is norm-euclidean. Furthermore, we prove an estimate D < 214 for all norm-euclidean fields Q( √ D). Subsequently, the case D ≡ 1 (mod 4) is discussed in detail. For the case D ≡ 1 (mod 4) we mention references to the results of other authors. 1
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See also: similar author names
10 ZEMKOVÁ, Kateřina
2 Zemková, Kamila
10 Zemková, Kateřina
2 Zemková, Klára
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