Abstract
Abstract
We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and use them to describe both the definable and classical Bohr compactifications of rings. We then use model-theoretic connected components to explicitly calculate Bohr compactifications of some classical matrix groups, such as the discrete Heisenberg group
${\mathrm {UT}}_3({\mathbb {Z}})$
, the continuous Heisenberg group
${\mathrm {UT}}_3({\mathbb {R}})$
, and, more generally, groups of upper unitriangular and invertible upper triangular matrices over unital rings.
Publisher
Cambridge University Press (CUP)
Cited by
4 articles.
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1. ON MODEL-THEORETIC CONNECTED GROUPS;The Journal of Symbolic Logic;2023-11-14
2. Locally compact models for approximate rings;Mathematische Annalen;2023-06-29
3. On Stable Quotients;Notre Dame Journal of Formal Logic;2022-08-01
4. Generating ideals by additive subgroups of rings;Annals of Pure and Applied Logic;2022-07