3 papers
math.GM2025
Inner products for strongly regular near-vector spaces and duality for finite dimensional near-vector spaces
Leeandro Boonzaaier, Sophie Marques, Daniella Moore
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly…
math.RA2025
Why is the category of near-vector spaces abelian?
Zurab Janelidze, Sophie Marques, Daniella Moore
In this paper we present a unified proof of the fact that the category of modules over a ring and the category of near-vector spaces in the sense of J. André, over an appropriate s…
math.RA2024
Distributive decomposition of near-vector spaces
Leandro Boonzaaier, Sophie Marques, Daniella Moore
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 distributiv…