Keywords
Abstract Algebra; Lattices; Prime Numbers; Units; Continued Fractions
Abstract
The failure of unique factorization in a ring leads to the investigation of the closest algebraic structure, which are prime ideals. Using generalizations that have helped solve questions such as Fermat's Last Theorem, there is interest to study the elements with a multiplicative inverse (units) via the geometry and arithmetic patterns that arise in quadratic integer rings, since they provide tools for other questions in mathematics, ranging from pure algebra to applications in cryptography, and more. Overall, the following thesis provides a small exposition on the theory of integral domains and some specific calculations.
Thesis Completion Year
2025
Thesis Completion Semester
Spring
Thesis Chair
Reid, Michael; Ghantous, Wissam
College
College of Sciences
Department
Mathematics
Thesis Discipline
Mathematics
Language
English
Access Status
Open Access
Length of Campus Access
None
Campus Location
Orlando (Main) Campus
Subjects
Algebraic number theory; Unit groups (Ring theory); Integral domains; Rings (Algebra); Dissertations, Academic--Mathematics
STARS Citation
Roca, Gabriel F., "Prime Factorization and Unit Calculations of Quadratic Integer Rings" (2025). Honors Undergraduate Theses. 296.
https://stars.library.ucf.edu/hut2024/296
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