| Type of Document |
Master's Thesis |
| Author |
Landquist, Eric Jon
|
| Author's Email Address |
elandqui@vt.edu |
| URN |
etd-05182000-12080004 |
| Title |
On Nonassociative Division Rings and Projective Planes |
| Degree |
Master of Science |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Farkas, Daniel R. |
Committee Chair |
| Brown, Ezra A. |
Committee Member |
| Green, Edward L. |
Committee Member |
|
| Keywords |
- division rings
- semifields
- projective planes
- nonassociative
|
| Date of Defense |
2000-05-18 |
| Availability |
unrestricted |
Abstract
An interesting thing happens when one begins with the axioms of a field, but does not require the associative and commutative properties. The resulting nonassociative division ring is referred to as a ``semifield" in this paper. Semifields have intimate ties to finite projective planes. In short, a finite projective plane with certain restrictions gives rise to a semifield, and, in turn, a finite semifield can be used via a coordinate construction, to build a special finite projective plane. It is also shown that two finite semifields provide a coordinate system for isomorphic projective planes if and only if the semifields are isotopic, where isotopy is a relationship similar to but weaker than isomorphism.
Before we prove those results, we explore the nature of isotopy to get a little better feel for the concept. For example, we look at isotopy for associative algebras. We will also examine a particular family of semifields and gather concrete information about solutions to linear equations and isomorphisms.
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| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
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| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
sfield.pdf |
233.62 Kb |
00:01:04 |
00:00:33 |
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