  This article answers a question that naturally arises from the articles by
Grabitz and Broussous "Pure elements and intertwining classes of simple strata
in local central simple algebras" and Broussous and Lemaire "Buildings of
GL(m,D) and Centralizers". For an Azumaya-Algebra A over a non-Archimedean
local field F, Grabitz and Broussous have introduced embedding invariants for
field embeddings, that is for pairs (E,a), where E is a field extension of F in
A, and $a$ is a hereditary order which is normalised by E^x. On the other hand
if we take such a field extension E and define B to be the centralizer of E in
A, then G:=A^x and G_E:=B^x are sets of rational points of reductive groups
defined over F and E respectively. Broussous and Lemaire have defined a map
j_E: I^{E^x}\to I_E, where $I$ is the the Euclidean building of $G$, and I_E is
the Euclidean building of G_E. The question which we address is to relate the
embedding invariants to the behavior of the map j_E with respect to the
simplicial structures of $I$ and I_E. I have to thank very much Prof. Zink from
Homboldt University Berlin for his helpful remarks, the revision of the work
and for giving my the interesting task.
