Near-vector spaces determined by finite fields and their fibrations

Howell, Karin-Therese (2019)

CITATION: Howell, K. T. 2019. Near-vector spaces determined by finite fields and their fibrations. Turkish Journal of Mathematics, 43: 2549-2560, doi:10.3906/mat-1905-110.

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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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