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Abstract
We study some one-sided ideals of row bounded and of column bounded matrix rings over free algebras. Obtained results are applied to answer several open problems on subhereditary radicals of associative rings. In particular we show that the right strongly prime radical is not left subhereditary and that the lattice of left (right) subhereditary radicals is not complete.
Acknowledgment
The third author was supported by KBN Grant 5 PO3A 041 20 and National Cheng-Kung University, Tainan, Taiwan.
Notes
# Communicated by M. Ferrero.