Identifier
etd-07072008-154718
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
This dissertation is concerned with providing a description of certain symmetric bilinear forms, called trace forms, associated with finite normal extensions N/K of an algebraic number field K, with abelian Galois group Gal(N/K). These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring W(K). Complete descriptions are obtained when the base field K has exactly one dyadic prime and either no real embeddings or one real embedding. For these fields K, the set of abelian trace forms is closed under multiplication in the Witt ring W(K).
Date
2008
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Smith, Karli, "Trace Forms of Abelian Extensions of Number Fields" (2008). LSU Doctoral Dissertations. 3627.
https://repository.lsu.edu/gradschool_dissertations/3627
Committee Chair
Robert Perlis
DOI
10.31390/gradschool_dissertations.3627