  We prove that the ring of polynomials in several commuting indeterminates
over a nil ring cannot be homomorphically mapped onto a ring with identity,
i.e. it is Brown-McCoy radical. It answers a question posed by Puczylowski and
Smoktunowicz. We also show that the central closure of a prime nil ring cannot
be a simple ring with identity solving a problem due to Beidar.
