On direct sums and quotient spaces of near-vector spaces.

Autor: Howell, K. -T., Cara, P., Wessels, L.
Zdroj: Afrika Matematica; Mar2024, Vol. 35 Issue 1, p1-13, 13p
Abstrakt: In 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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