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dc.contributor Graduate Program in Mathematics.
dc.contributor.advisor Beyarslan, Özlem.
dc.contributor.advisor Özman, Ekin.
dc.contributor.author Değirmenci, Pınar.
dc.date.accessioned 2023-10-15T11:13:22Z
dc.date.available 2023-10-15T11:13:22Z
dc.date.issued 2022
dc.identifier.other MATH 2022 D44
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/19900
dc.description.abstract Determining whether the ring of integers OK of an algebraic number field K of degree n admits a power integral basis is one of the classic problems in algebraic number theory. In other words, we want to determine whether there exists α ∈ OK such that {1, α, . . . , αn−1} is a Q-basis for K. This question dates back to the 1960s and was introduced by a German mathematician, Helmut Hasse. In this thesis, we will study the monogenicity of cubic number fields and their lift to monogenic sextic number fields. After recalling some background material on algebraic number theory and related topics, we will focus on specific cubic fields such as pure cubic fields and cyclic cubic fields. Next, we will study the lifting of all monogenic cyclic cubic fields to monogenic sextic fields. This thesis was supported by Bo˘gazi¸ci University Research Fund Grant Number 19082.
dc.publisher Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022.
dc.subject.lcsh Blowing up (Algebraic geometry)
dc.subject.lcsh Algebraic number theory.
dc.title Monogenic number fields
dc.format.pages x, 62 leaves


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