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On rings whose prime ideals are completely prime. (English) Zbl 1024.16002

For a ring \(R\), the prime radical and the set of all nilpotent elements are denoted by \(P(R)\) and \(N(R)\). A proper two-sided ideal \(I\) of a ring \(R\) is called 2-primal if \(P(R/I)=N(R/I)\). A ring \(R\) is called strongly 2-primal if every proper two-sided ideal of \(R\) is 2-primal. Strongly 2-primal rings with several kinds of \(\pi\)-regularities are studied.
Reviewer: J.K.Park (Pusan)

MSC:

16D25 Ideals in associative algebras
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16N60 Prime and semiprime associative rings
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References:

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