4 papers
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…
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…
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…
A note on the transport of (near-)field structures
L. Boonzaaier, S. Marques
This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this…