On representation theory and near-vector spaces

Howell, Karin-Therese; Chistyakov, D. S.; Sanon, Sogo Pierre

doi:10.1080/03081087.2018.1459449

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Finite Dimensional Near-vector Spaces Constructed Using Fini1

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Cited by 5 publications

(2 citation statements)

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“…It characterises regularity for these near-vector spaces. In fact, in [2] using this theorem it is shown that if A 1 , A 2 , . .…”

Section: Finite Dimensional Near-vector Spaces Constructed Using Finimentioning

confidence: 99%

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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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“…It characterises regularity for these near-vector spaces. In fact, in [2] using this theorem it is shown that if A 1 , A 2 , . .…”

Section: Finite Dimensional Near-vector Spaces Constructed Using Finimentioning

confidence: 99%

“…[2],Lemma 5.8, p.11) Let F = GF (p r ) and V = F n be a near-vector space with scalar multiplication defined for all α ∈ F by(x 1 , . .…”

mentioning

confidence: 99%

Near-vector spaces determined by finite fields and their fibrations

Howell¹

2019

Turk J Math

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On direct sums and quotient spaces of near-vector spaces

Howell,

Cara,

Wessels

2024

Afr. Mat.

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In this paper we study the direct sums of subspaces and some constructions of quotient spaces of near-vector spaces, as defined by André. In particular, for near-vector spaces constructed by taking copies of finite fields, we characterise the quasi-kernels of their quotient spaces, find their cardinality and determine when they are regular. In the case of non-regular quotient spaces, we show how they decompose into maximal regular subspaces. We show how the theory of finite-dimensional near-vector spaces constructed from finite fields allows us to reconstruct near-vector spaces with certain quotient spaces.

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On counting subspaces of Near-vector Spaces

Sanon

2020

Discrete Mathematics

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On representation theory and near-vector spaces

Cited by 5 publications

References 5 publications

Near-vector spaces determined by finite fields and their fibrations

Near-vector spaces determined by finite fields and their fibrations

On direct sums and quotient spaces of near-vector spaces

On counting subspaces of Near-vector Spaces

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