Isomorphisms between strongly triangular matrix rings

We describe isomorphisms between strongly triangular matrix rings that were defined earlier in Birkenmeier et al. (2000) [3], 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, which completes the project started in Anh and van Wyk (2011) [1].