East Asian mathematical journal
- Volume 18 Issue 1
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- Pages.15-20
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- 2002
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
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)
- Published : 2002.06.27
Abstract
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.