4 papers
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…
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…
Near-field structures on a given scalar group
Sophie Marques, Leandro Boonzaaier
With this paper, we gain a better understanding of the set of near-field structures on a fixed scalar group. If we were able to describe all near-field structures on a fixed scalar…
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…