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There are presented some generalizations and extensions of results for rings which are sums of two or tree subrings. It is provided a new proof of the well-known Kegel’s result stating that a ring being a sum of two nilpotent subrings is itself nilpotent. Moreover, it is proved that if R is a ring of the form $R=A+B$, where A is a subgroup of the additive group of R satisfying $A^d\subseteq B$ for some positive integer d and B is a subring of R such that $B\in S$, where S is N-radical contained in the class of all locally nilpotent rings, then $R\in S$.

This article is devoted to the historical study of the ADS-problem with a special emphasis on the use of methods and techniques, emerging with the development of the theory of rings: accessible subrings, iterated maximal essential extensions of rings, completely normal rings. We construct new examples of classes for which Kurosh’s chain stabilizes at any given step. We recall the old nontrivial questions, and we pose a new one.

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On rings which are sums of subrings

ACCESSIBLE SUBRINGS AND KUROSH’S CHAINS OF ASSOCIATIVE RINGS

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2 results

On rings which are sums of subrings

ACCESSIBLE SUBRINGS AND KUROSH’S CHAINS OF ASSOCIATIVE RINGS