On the Theory of Near-Vector Spaces

Howell, Karin-Therese; Chistyakov, D. S.

doi:10.1007/s10958-018-3755-7

Cited by 5 publications

(9 citation statements)

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“…Later André [1] introduced another notion of near-vector spaces and used automorphisms in the construction. André's version has been studied in many papers, and theses, for example [10] while Beidleman near-vector spaces had not since his thesis until recently the authors of [4] added to the body of existing work.…”

Section: Introductionmentioning

confidence: 99%

On the generalized distributive set of a finite nearfield

Djagba

2020

Journal of Algebra

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For any nearfield (R, +, •), denote by D(R) the set of all distributive elements of R. Let R be a finite Dickson nearfield that arises from Dickson pair (q, n). For a given pair (α, β) ∈ R 2 we study the generalized distributive set•" is the multiplication of the Dickson nearfield. We find that D(α, β) is not in general a subfield of the finite field F q n . In contrast to the situation for D(R), we also find that D(α, β) is not in general a subnearfield of R. We obtain sufficient conditions on α, β for D(α, β) to be a subfield of F q n and derive an algorithm that tests if D(α, β) is a subfield of F q n or not. We also study the notions of R-dimension, R-basis, seed sets and seed number of R-subgroups of the Beidleman near-vector spaces R m where m is a positive integer. Finally we determine the maximal R-dimension of gen(v 1 , v 2 ) for v 1 , v 2 ∈ R m , where gen(v 1 , v 2 ) is the smallest R-subgroup containing the vectors v 1 and v 2 .

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Section: Introductionmentioning

confidence: 99%

On the generalized distributive set of a finite nearfield

Djagba

2020

Journal of Algebra

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Section: Introductionmentioning

confidence: 99%

“…Subsequently, several researchers like Whaling, André, and Karzel introduced a similar notion in different ways. André near-vector spaces have been studied in many papers (for example [2,9,3]). In this paper, we add to the theory of near-vector spaces originally defined by Beidleman. As in [3] for André near-vector spaces, we investigate the subspace structure of Beidleman near-vector spaces and highlight differences and similarities between these two types of near-vector spaces.…”

Section: Introductionmentioning

confidence: 99%

The subspace structure of finite dimensional Beidleman near-vector spaces

Djagba

Howell

2019

Linear and Multilinear Algebra

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The subspace structure of Beidleman near-vector spaces is investigated. We characterise finite dimensional Beidleman near-vector spaces and we classify the R-subgroups of finite dimensional Beidleman near-vector spaces. We provide an algorithm to compute the smallest R-subgroup containing a given set of vectors. Finally, we classify the subspaces of finite dimensional Beidleman 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%