Multiplicative near-vector spaces

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.