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Pythagoras numbers of orders in number fields
Hájková, Veronika ; Kala, Vítězslav (advisor) ; Krásenský, Jakub (referee)
This thesis deals with the investigation of Pythagoras numbers of orders in number fields. After a short introduction, where I repeat and define new concepts important for understanding this work, I deal with the necessary characteristics of the trace. The thesis further proves the existence of orders in totally real number fields whose Pythagoras numbers are arbitrarily large and ends with a proof that for any N ∈ N, there is a totally real number field whose maximum order has a Pythagoras number of at least N. 1

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