BOHR COMPACTIFICATIONS OF GROUPS AND RINGS

Abstract We introduce and study model-theoretic connected components of rings as an analogue definable groups. develop their basic theory use them to describe both the classical Bohr compactifications rings. then explicitly calculate some matrix groups, such discrete Heisenberg group ${\mathrm {UT}}_3({\mathbb {Z}})$ , continuous {R}})$ and, more generally, groups upper unitriangular invertible triangular matrices over unital