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A topological prime quasi-radical

Abstract

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.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 11–22, 2004.

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Bazigaran, B., Glavatsky, S.T. & Mikhalev, A.V. A topological prime quasi-radical. J Math Sci 139, 6663–6671 (2006). https://doi.org/10.1007/s10958-006-0383-4

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Keywords

  • Prime Ideal
  • Identity Element
  • Left Ideal
  • Closed Ideal
  • Matrix Ring