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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…
math.RA2022
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…