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On right ideals of a ring close to von Neumann ones. (Russian) Zbl 0721.16002
A right ideal P of an associative ring R is said to be strongly von Neumann if for every \(a\in R\) there exists \(x\in R\) such that axa-a\(\in P\) and axP\(\subseteq P\). It is shown that every intersection of finitely many maximal modular right ideals of R is a strongly von Neumann right ideal of R. Moreover, every strongly von Neumann right ideal P of R is the intersection of all maximal modular right ideals of R containing P, so that the Jacobson radical of R coincides with the intersection of all strongly von Neumann right ideals of R.
MSC:
16D25 Ideals in associative algebras
16N20 Jacobson radical, quasimultiplication
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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