On Subspaces and Mappings of Near-vector Spaces

Howell, Karin-Therese

doi:10.1080/00927872.2014.900689

Cited by 17 publications

(19 citation statements)

References 3 publications

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“…Example 5.14. Let R = DN (3, 2) be the finite Dickson nearfield that arises from the pair (3,2) and v 1 = (1, 1, 2, x+1, 1), v 2 = (0, 0, 0, 2x+2, 1), v 3 = (1, 1, 1, x+2, 1) ∈ R 5 . By Theorem 5.12, we have…”

Section: It Follows Thatmentioning

confidence: 99%

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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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Section: It Follows Thatmentioning

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.…”

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 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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“…These results were extended in [8] to all finite dimensional near-vector spaces over arbitrary finite fields. In [6] homogeneous and linear mappings and subspaces were investigated.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we begin with some preliminary material in section 2.1. on nearvector spaces and prove some properties of isomorphisms of near-vector spaces. In section 2.2. we generalise a construction that was first considered in [6] and in section 2.3. we focus on nearrings of quotients, giving some new results that allow for alternative proofs of some of the main known results. In section 2.…”

Section: Introductionmentioning

confidence: 99%