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The main goal of this paper is to prove a correct version of one of the main results in the paper Note on some ideals of associative rings by M. Filipowicz, M. Kępczyk [Acta Math. Hungar. 142 (2014), 72–79]. Moreover, we give a new proof of Theorem 8 there.

A note on $*(x,y,z)$-simple rings