  If Y,Z are three-dimensional smooth varieties related by a flop, then Bondal
and Orlov conjectured that the derived categories of coherent sheaves on Y and
Z are equivalent. This conjecture was recently proved by Bridgeland. Our aim in
this paper is to give a partially new proof of Bridgeland's result using
non-commutative rings. The new proof also covers some mild singular and higher
dimensional situations (including the one in the recent paper by Chen: ``Flops
and Equivalences of derived Categories for Threefolds with only Gorenstein
Singularities'').
