Topological incidence rings, their groups of units and incidence functors
Abstract
We focus on working on incidence rings and their group of units. Some general properties about them are given, including how they are always the inverse limit of finite matrix groups/rings, giving a natural way to define their topology. Such construction can also be translated as a functor from the category of locally finite, preordered sets to the category of topological rings. It is shown that under some assumptions on the ordered sets, simple matrix groups over a field can be built from the group of units of such rings.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2023
- DOI:
- 10.48550/arXiv.2310.13238
- arXiv:
- arXiv:2310.13238
- Bibcode:
- 2023arXiv231013238E
- Keywords:
-
- Mathematics - Group Theory;
- 20H25;
- 20E32;
- 06A06;
- 06E20;
- 16B50;
- 16W80;
- 16S50
- E-Print:
- 35 pages