1 results
On rings which are sums of subrings
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 21 February 2025, pp. 1-9
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- Article
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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 
$R\in S$.
