**On generating ideals by additive subgroups of rings and an application to**

Bohr compactifications of some matrix groups

Bohr compactifications of some matrix groups

Abstract:

I will present several fundamental results about generating ideals in

finitely many steps inside additive groups of rings from my very recent

joint paper with T. Rzepecki. I will also mention an application to

computations of definable and classical Bohr compactifications of the

groups of upper unitriangular and invertible upper triangular matrices

over arbitrary unital rings, based on my joint paper with J. Gismatullin

and G. Jagiella. An essential role in this research is played by

model-theoretic connected components of definable groups and rings. In

particular, these components are used to compute the above Bohr

compactifications. Regarding connected components, roughly speaking, one

of our main results says that the type-definable connected component of

the additive subgroup of a definable (saturated) unital ring generates an

ideal in finitely many steps (and so this generated ideal is exactly the

ring type-definable connected component).

## Date:

Wed, 13/01/2021 - 11:15 to 13:00

## Location:

https://huji.zoom.us/j/82821066522?pwd=aVJnTkxBYktycHdzNFN5WDV0R2FkZz09