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)


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
Full Text: DOI


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