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.