The decomposition of finite-dimensional near-vector spaces

Dorfling, Samantha; Howell, Karin-Therese; Sanon, Sogo Pierre

doi:10.1080/00927872.2017.1404083

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…Definition 2.1. [5] A set V is said to be a right vector space over a division ring F, if ( ) , V + is an abelian group and, if for each F α ∈ and v V ∈ , there is a unique element v V α ∈ such that the following conditions hold for all , F α β ∈ and all ,…”

Section: Basic Definitionsmentioning

confidence: 99%

Near-Vector Spaces Constructed over Zp, for p a Prime

Tefoetsile¹,

Kalunga²,

Zimba³

et al. 2023

APM

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The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with p  for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

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Section: Basic Definitionsmentioning

confidence: 99%

Near-Vector Spaces Constructed over Zp, for p a Prime

Tefoetsile¹,

Kalunga²,

Zimba³

et al. 2023

APM

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“…The near-vector spaces we study in this paper were first introduced by André [1] in 1974. Their subspaces and mappings were studied in [5] and their decomposition in [3]. Near-vector spaces constructed from finite fields were characterised in [6] and more recently in [11] the number of near-vector spaces constructed from finite fields were counted.…”

Section: Introductionmentioning

confidence: 99%

Near-vector spaces determined by finite fields and their fibrations

Howell¹

2019

Turk J Math

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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.

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“…His near-vector spaces have less linearity than normal vector spaces. They have been studied in several papers, including [2][3][4][5][6]. More recently, since André did a lot of work in geometry, their geometric structure has come under investigation.…”

Section: Introductionmentioning

confidence: 99%