Distribution and generalized centre in planar nearrings

Boykett, Tim

doi:10.14232/actasm-018-036-y

Cited by 3 publications

(3 citation statements)

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“…However, this counterexample is still in fact a vector space, it is a vector space over the field (F, •, + u ), where for α, β ∈ F , we have α + u β = (α 3 + β 3 ) 1 3 . This field is in fact isomorphic to (R, •, +) via the map taking α to α 3 .…”

Section: Commutative Near Vector Spacesmentioning

confidence: 99%

“…These results were extended to all finite dimension near vector spaces over arbitrary finite fields in [7]. Near vector spaces have been used in cryptography (see [4]) and to construct an interesting new class of planar nearrings (see [3]). Our aim in this paper is to use Model theory to add to the theory and understanding of near vector spaces.…”

Section: Introductionmentioning

confidence: 99%

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On the Theory of Near-Vector Spaces

Howell

Chistyakov

2018

J Math Sci

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In this paper we study near vector spaces over a commutative F from a model theoretic point of view. In this context we show regular near vector spaces are in fact vector spaces. We find that near vector spaces are not first order axiomatisable, but that finite block near vector spaces are. In the latter case we establish quantifier elimination, and that the theory is controlled by which elements of the pointwise additive closure of F are automorphisms of the near vector space.

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Section: Commutative Near Vector Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Theory of Near-Vector Spaces

Howell

Chistyakov

2018

J Math Sci

View full text Add to dashboard Cite

show abstract

“…Recently, near-vector spaces have been used in several applications, including in secret sharing schemes in cryptography [4] and to construct interesting examples of families of planar nearrings [3]. In addition, they have proved interesting from a model theory perspective too [2].…”

Section: Introductionmentioning

confidence: 99%