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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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