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