除环上的微积分引论
Introduction into Calculus over Division Ring
摘要：
基于阿贝尔群中除环的孪生表示，考虑了除环上的$D$-\Hyph向量空间. $D$ \Hyph向量空间的态射是$D$ \Hyph向量空间的线性映射。本文认为连续除环的函数$f$的导数是最接近函数$f$的线性映射。探讨了映入泰勒级数展开和微分方程的求解方法。$D$ \Hyph向量空间中的范数允许考虑$D$ \Hyph向量空间的连续映射。定义$D$ \Hyph向量空间的映射$f$的微分为最接近映射$f$的线性映射。
英文摘要：
Based on twin representations of division ring in an Abelian group I consider $D$\Hyph vector spaces over division ring. Morphism of $D$\Hyph vector spaces is linear map of $D$\Hyph vector spaces. I consider derivative of function $f$ of continuous division ring as linear map the most close to function $f$. I explore expansion of map into Taylor series and method to find solution of differential equation. The norm in $D$\Hyph vector space allows considering of continuous mapping of $D$\Hyph vector spaces. Differential of mapping $f$ of $D$\Hyph vector spaces is defined as linear mapping the most close to map $f$.
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