On the Baer rings (Q793128)

Let R be a (not necessarily commutative) ring with unit and without nonzero nilpotent elements. The author proves that R is a weak Baer ring (i.e. the annihilator of each element of R is generated by an idempotent) if and only if every prime ideal contains a unique minimal prime and the space of minimal primes is compact in the hull-kernel topology.