On spanning sets and generators of near-vector spaces

Abstract

In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.

Toward an intuitive understanding of the structure of near-vector spaces

“…Definition 2.4. ( [10], Definition 3.2, p.3235) Let (V, A) be a near-vector space, then the span of a set S of vectors is defined to be the intersection W of all subspaces of V that contain S, denoted span S.…”