A decomposition theorem for semiprime rings - Khibina, M. (Algebra and Discrete Mathematics, 2005)
A ring A is called an F DI-ring if there exists
a decomposition of the identity of A in a sum of finite number
of pairwise orthogonal primitive idempotents. We call a primitive idempotent e artinian if the ring eAe is Artinian. We prove
that every semiprime F DI-ring is a direct product of a semisimple
Artinian ring and a semiprime F DI-ring whose identity decomposition doesn’t contain artinian idempotents.