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Short proof of a conjecture concerning split-by-nilpotent extensions


Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E. We provide a short proof to a conjecture by Assem and Zacharia concerning properties of \(\mathop {\text {mod}}B\) inherited by \(\mathop {\text {mod}}C\). We show if B is a tilted algebra, then C is a tilted algebra.

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Correspondence to Stephen Zito.

Additional information

The author was supported by the University of Connecticut-Waterbury.

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Zito, S. Short proof of a conjecture concerning split-by-nilpotent extensions. Arch. Math. 111, 479–483 (2018).

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Mathematics Subject Classification

  • 16G20
  • 16G70


  • Split-by-nilpotent extensions
  • Tilted algebras