Introduction into Calculus over Division Ring

Details Introduction into Calculus over Division Ring Introduction into Calculus over Division Ring

2008-12-30

arxiv.org/abs/0812.4763v6

Mathematics

General Mathematics

English text - 97 pages; Russian text - 103 pages. Version 3: Considered definition of Taylor series and integral

Scientific paper

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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