On a generalization of hall quasifields
Date of Publication
1995
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Dr. Arlene Pascasio
Defense Panel Chair
Dr. Severino Diesto
Defense Panel Member
Dr. Blessilda Raposa
Clarence Tan
Abstract/Summary
The thesis is an exposition of an article entitled A Generalization of Hall Quasifields by Yutaka Hiramine. Quasifields are algebraic structures intimately connected with the study and construction of non-desarguesian translation planes. Two major results about quasifields are hereby presented in a more comprehensible mathematical language. The first is a theorem that generalizes Hall quasifields in such a way that the quasifieds corresponding to the spread sets constructed by Narayana Rao and Satyanarayana are included. The other is a theorem that provides a form for the mappings defined in the first theorem. Some basic concepts in projective geometry and algebra that are relevant to this work are exhibited and discussed. These include projective and affine planes and the construction of these planes from vector spaces, collineations, desarguesian and translation planes, quasifields, spreads and spread sets. A comprehensive account of the Bruck and Bose construction of translation planes is also presented.
Abstract Format
html
Language
English
Format
Accession Number
TG02387
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
173 leaves
Keywords
Translation planes; Geometry; Affine; Geometry; Projective; Fields; Algebraic
Recommended Citation
Elvira, D. T. (1995). On a generalization of hall quasifields. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1660
