Introduction into Calculus over Division Ring
Abstract
Based on twin representations of division ring in an Abelian group I consider \Hyph vector spaces over division ring. Morphism of \Hyph vector spaces is linear map of \Hyph vector spaces. I consider derivative of function of continuous division ring as linear map the most close to function . I explore expansion of map into Taylor series and method to find solution of differential equation. The norm in \Hyph vector space allows considering of continuous mapping of \Hyph vector spaces. Differential of mapping of \Hyph vector spaces is defined as linear mapping the most close to map .
Cite
@article{arxiv.0812.4763,
title = {Introduction into Calculus over Division Ring},
author = {Aleks Kleyn},
journal= {arXiv preprint arXiv:0812.4763},
year = {2013}
}
Comments
English text - 97 pages; Russian text - 103 pages. Version 3: Considered definition of Taylor series and integral. arXiv admin note: text overlap with arXiv:math/0701238, arXiv:0908.3307, arXiv:1006.2597