Kaplansky's conjecture on von Neumann regular rings

Let $R$ be a ring. A ring is von Neumann regular if for every $a\in R$ there exists $b\in R$ such that $a=aba$; it is semiprime if it has no nonzero nilpotent ideals, and a prime factor ring is a quotient $R/P$ by a prime ideal $P$.

Kaplansky's conjecture. $R$ is von Neumann regular if and only if $R$ is semiprime and each prime factor ring of $R$ is von Neumann regular.

Kaplansky formulated this characterization, which was subsequently proved by J. W. Fisher and R. L. Snider. Thus the conjecture is solved.