Distributive decomposition of near-vector spaces

2024/07/24 by Boonzaaier, Leandro, Marques, Sophie, Moore, Daniella · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2407.17134

Abstract

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of the dimension of these summands. These results offer new insights into the structure and properties of near-vector spaces.

Cited by

• Inner products for strongly regular near-vector spaces and duality for finite dimensional near-vector spaces

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