Browsing by Author "Sanon, Sogo Pierre"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
- ItemContributions to the theory of near-vector spaces(Stellenbosch : Stellenbosch University, 2017-12) Sanon, Sogo Pierre; Howell, Karin-Therese; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.ENGLISH ABSTRACT : The purpose of this thesis is to give an exposition and expand the theory of near-vector spaces. Near-vector space theory is a new and rich field of mathematics and has been used in several applications, including in secret sharing schemes in cryptography and to construct interesting new examples of planar near-rings. There are two type of near-vector spaces, we focus on the near-vector space defined by André in [2]. After giving several elementary definitions and properties in Chapter 2, we present the theory of nearvector spaces in Chapter 3. In [13] van der Walt showed how to construct an arbitrary finite-dimensional near-vector space, using a finite number of near-fields, all having isomorphic multiplicative semigroups. The majority of the results did not contain complete proofs and explanation. Chapter 4 is dedicated to the proofs and explanations of these results. In Chapter 5 we investigate the linear mappings of near-vector spaces. New results are presented in this section which have been accepted for publication.
- ItemNear-vector spaces constructed from near domains(Miskolci Egyetemi Kiado, 2018) Howell, Karin-Therese; Sanon, Sogo PierreIn this paper we prove some new results on near-vector spaces and near domains and give a first application of the nearring of quotients with respect to a multiplicative set, namely we construct a new class of near-vector spaces from near domains.
- ItemOn spanning sets and generators of near-vector spaces(Scientific and Technological Research Council of Turkey, 2018) Howell, Karin-Therese; Sanon, Sogo PierreIn this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.