Abstract
AbstractIn this paper we study the direct sums of subspaces and some constructions of quotient spaces of near-vector spaces, as defined by André. In particular, for near-vector spaces constructed by taking copies of finite fields, we characterise the quasi-kernels of their quotient spaces, find their cardinality and determine when they are regular. In the case of non-regular quotient spaces, we show how they decompose into maximal regular subspaces. We show how the theory of finite-dimensional near-vector spaces constructed from finite fields allows us to reconstruct near-vector spaces with certain quotient spaces.
Funder
National Research Foundation
Stellenbosch University
Publisher
Springer Science and Business Media LLC
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