### On the map between homology of henselization and completion of some local rings, by G. Banaszak, W. Gajda, and P. Krason

In this note we prove that the integral homology of the
special linear group of the henselization of some local rings
imbeds into the homology of the special linear group of the completion.

We define henselian adele ring and prove that the integral
homology of its special linear group injects into the homology of $Sl$
of the finite adele ring. The method of the proof is based on an
application of the Artin approximation theorem to the bar complex which
calculates the homology.

G. Banaszak <banaszak@math.amu.edu.pl>

W. Gajda <gajda@math.amu.edu.pl>

P. Krason <krason@uoo.univ.szczecin.pl>