Title: Multiplicative near-vector spaces Show Chinese title

Title: 乘性近向量空间

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. Show Chinese abstract

Abstract: 近向量空间将线性代数工具扩展到非线性的代数结构中，从而使得非线性问题的研究成为可能。然而，明确的构造方法仍然很少见。 本文介绍了一类广泛的可计算的近向量空间族，称为乘法型，并探讨了它们的性质。这个族在有限域、实数域和复数域上完全确定。 我们还讨论了近向量空间范畴中无限余积和积的存在性。 最后，我们引入了实数域上乘法型近向量空间的复化。