Near-vector spaces determined by finite fields and their fibrations
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Scientific and Technological Research Council of Turkey
Scientific and Technological Research Council of Turkey
Scientific and Technological Research Council of Turkey
Abstract
In this paper we study near-vector spaces constructed from copies of finite fields. We show that for these near-vector spaces regularity is equivalent to the quasikernel being the entire space. As a second focus, we study the fibrations of near-vector spaces. We define the pseudo-projective space of a near-vector space and prove that a special class of near-vector spaces, namely those constructed using finite fields, always has a fibration associated with them. We also give a formula for calculating the cardinality of the pseudo-projective space for this class of near-vector spaces.
Description
CITATION: Howell, K. T. 2019. Near-vector spaces determined by finite fields and their fibrations. Turkish Journal of Mathematics, 43: 2549-2560, doi:10.3906/mat-1905-110.
The original publication is available at http://journals.tubitak.gov.tr
The original publication is available at http://journals.tubitak.gov.tr
Keywords
Near-vector spaces, Vector spaces, Finite fields (Algebra), Fibrations, Kernal functions, Directed graphs
Citation
Howell, K. T. 2019. Near-vector spaces determined by finite fields and their fibrations. Turkish Journal of Mathematics, 43: 2549-2560, doi:10.3906/mat-1905-110