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

Abstract

In this article we analyze the definition André 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.

Keywords:

• Near-vector spaces
• nearrings
• nearfields
• division rings
• span
• subspaces
• linear a + lgebra

2020 Mathematics Subject Classification:

• 16Y30
• 12K05

Acknowledgments

The authors would like to thank Charlotte Kestner for Example 3.6 and Jacques Rabie for Example 3.5 and his helpful comments.

Additional information

Funding

The authors would like to express their gratitude for funding to the National Research Foundation (South Africa), Grant number 93050.