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
Multiplicative near-vector spaces
L. Boonzaaier, S. Marques, D. Moore
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This pape…
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…