On distant-isomorphisms of projective lines
Algebraic Geometry
2024-02-13 v1 Rings and Algebras
Abstract
We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorphic to a field, every distant isomorphism arises from a Jordan isomorphism of rings and a projectivity. We show this by virtue of a one-one correspondence linking the projective line over a semisimple ring with a Segre product of Grassmann spaces.
Cite
@article{arxiv.1304.0226,
title = {On distant-isomorphisms of projective lines},
author = {Andrea Blunck and Hans Havlicek},
journal= {arXiv preprint arXiv:1304.0226},
year = {2024}
}