A topological prime quasi-radical

In this paper, we consider a topological prime quasi-radical μ(R), which is the intersection of closed prime ideals in a topological ring R. Examples are given that show that μ(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. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 11–22, 2004.