On rings which are sums of subrings
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 874-882
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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 $R\in S$.
Andruszkiewicz, Ryszard R.; Kȩpczyk, Marek. On rings which are sums of subrings. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 874-882. doi: 10.4153/S0008439525000177
@article{10_4153_S0008439525000177,
author = {Andruszkiewicz, Ryszard R. and K\c{e}pczyk, Marek},
title = {On rings which are sums of subrings},
journal = {Canadian mathematical bulletin},
pages = {874--882},
year = {2025},
volume = {68},
number = {3},
doi = {10.4153/S0008439525000177},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000177/}
}
TY - JOUR AU - Andruszkiewicz, Ryszard R. AU - Kȩpczyk, Marek TI - On rings which are sums of subrings JO - Canadian mathematical bulletin PY - 2025 SP - 874 EP - 882 VL - 68 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000177/ DO - 10.4153/S0008439525000177 ID - 10_4153_S0008439525000177 ER -
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