Logic Seminar - Krzysztof Krupinski

On generating ideals by additive subgroups of rings and an application to
Bohr compactifications of some matrix groups

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).


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