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

Karin-Therese Howell; Sophie Marques

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arXiv · 1912.06674

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

Karin-Therese Howell·Sophie Marques

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Abstract

In this paper, we analyze the definition Andr\'e proposed for near-vector spaces to make it more transparent. We also study the class of near-vector spaces over division rings and give a characterization of regularity that gives a new insight into the decomposition of near-vector spaces into regular subspaces. We explicitly describe span and deduce a new characterization of subspaces.

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Karin-Therese Howell, Sophie Marques. 2019-12-13. Toward an intuitive understanding of the structure of near-vector spaces. https://arxiv.org/abs/1912.06674

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