East Asian mathematical journal

  • 제18권1호
  • /
  • Pages.15-20
  • /
  • 2002
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지

RINGS IN WHICH NILPOTENT ELEMENTS FORM AN IDEAL

  • Cho, June-Rae (Department of Mathematics Pusan National University) ;
  • Kim, Nam-Kyun (Division of General Education Hanbat National University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University)
  • 발행 : 2002.06.27
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초록

We study the relationships between strongly prime ideals and completely prime ideals, concentrating on the connections among various radicals(prime radical, upper nilradical and generalized nilradical). Given a ring R, consider the condition: (*) nilpotent elements of R form an ideal in R. We show that a ring R satisfies (*) if and only if every minimal strongly prime ideal of R is completely prime if and only if the upper nilradical coincides with the generalized nilradical in R.

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