  We describe isomorphisms between strongly triangular matrix rings that were
defined earlier in Berkenmeier et al. (2000) as ones having a complete set of
triangulating idempotents, and we show that the so-called triangulating
idempotents behave analogously to idempotents in semiperfect rings. This study
yields also a way to compute theoretically the automorphism groups of such
rings in terms of corresponding automorphism groups of certain subrings and
bimodules involved in their structure.
