Publication Date
Summer 7-28-2020
Abstract
An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.
Degree Name
Mathematics
Level of Degree
Masters
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Janet Vassilev
Second Committee Member
Hongnian Huang
Third Committee Member
Alexandru Buium
Language
English
Keywords
Lattice, Prime Splitting Type, Quadratic Orders
Document Type
Thesis
Recommended Citation
Bridges, Ryan. "Lattice of Maximal-Primary Ideals in Quadratic Orders." (2020). https://digitalrepository.unm.edu/math_etds/153
