论文标题
组和戒指的玻尔压缩
Bohr compactifications of groups and rings
论文作者
论文摘要
我们介绍和研究环的模型连接的环组成部分，作为可定义组的模型理论连接组件的类似物。我们开发了他们的基本理论，并利用它们来描述环的可定义和经典的玻璃重压。然后，我们使用模型理论连接的组件来明确计算某些经典矩阵组的BOHR压缩，例如离散的Heisenberg Group $ ut_3（Z）$，连续的Heisenberg $ ut_3（r）$，以及更一般的上Unitriangulariangulariangulariangulariangular和Intrantian-trian-triangular Matrices cofterial rings and Inmitial rists consection $ ut_3（r）$。
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 $UT_3(Z)$, the continuous Heisenberg group $UT_3(R)$, and, more generally, groups of upper unitriangular and invertible upper triangular matrices over unital rings.
