Year: 2025
Type: preprint
Abstract: 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 paper introduces a broad computable family of near-vector spaces, called multiplicative, and explores their properties. This family is fully determined over finite, real, and complex fields. We also discuss the existence of infinite coproducts, and products in the category of near-vector spaces. Finally, we introduce the complexification of a multiplicative near-vector space over the real numbers.
Source: arXiv (Cornell University)
Authors: Boonzaaier, L., Marques, S., Moore, D.
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415979335
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