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.
Near-vector spaces, nearfields, near-vector space fibrations
"Near-vector spaces determined by finite fields and their fibrations,"
Turkish Journal of Mathematics: Vol. 43:
5, Article 38.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss5/38