A topological prime quasiradical

In this paper, we consider a topological prime quasi-radical $\mu(R)$, which is the intersection of closed prime ideals in a topological ring $R$. Examples are given that show that $\mu(R)$ is different from those topological analogs of the prime radical that have been studied earlier. The topological prime quasi-radicals of matrix rings and rings of polynomials are investigated.