English

Introduction into Geometry over Division Ring

General Mathematics 2024-10-22 v5

Abstract

Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the notion of tower of representations of F_i-algebras, i=1, ..., n, as the set of coordinated representations of F_i-algebras. I explore the geometry of affine space as example of tower of representations. Exploration of curvilinear coordinates allows us to see how look at the main structures of the manifold with affine connection. I explore Euclidean space over division ring.

Keywords

Cite

@article{arxiv.0906.0135,
  title  = {Introduction into Geometry over Division Ring},
  author = {Aleks Kleyn},
  journal= {arXiv preprint arXiv:0906.0135},
  year   = {2024}
}

Comments

English text - 50 pages; Russian text - 52 pages. Version 2: explored curvilinear coordinates in D-affine space

R2 v1 2026-06-21T13:08:02.661Z