A correction of the decomposability result in a paper by Meyer-Neutsch

@inproceedings{Tkachev2018ACO,
  title={A correction of the decomposability result in a paper by Meyer-Neutsch},
  author={Vladimir Gennad'evich Tkachev},
  year={2018}
}
In this short note, it is shown that there is a gap in the proof of Theorem 11 in the paper of Meyer and Neutsch (J. of Algebra, 1993). We prove, nevertheless, that the statement of the theorem is true and fix the proof by using a certain extremal property of idempotents which has an independent interest. 
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