Introduction into Calculus over Division Ring

Aleks Kleyn

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arXiv · 0812.4763

Introduction into Calculus over Division Ring

Aleks Kleyn

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Abstract

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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Aleks Kleyn. 2013-02-26. Introduction into Calculus over Division Ring. https://arxiv.org/abs/0812.4763

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