Dissertation/Thesis Abstract

Affine geometry over fields
by Boogar, Tyler E., M.S., California State University, Long Beach, 2014, 72; 1567944
Abstract (Summary)

We will use axiomatic systems to explore properties of affine and projective planes. The emphasis will be on the relationship between the number of lines and the number of points in a finite plane. We will then generalize affine space over an arbitrary field F and dimension n. The discussion of affine space will lead to a family of functions called collineations. These are the bijective functions which map any 3 points on a line to 3 points on another line. We will conclude with an attempt to classify all collineations as linear transformations up to automorphisms of the field F.

Indexing (document details)
Advisor: Mena, Robert
Commitee: Brevik, John, Murray, Will
School: California State University, Long Beach
Department: Mathematics and Statistics
School Location: United States -- California
Source: MAI 53/06M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Affine, Collineation, Projective
Publication Number: 1567944
ISBN: 978-1-321-29621-1
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