  I propose a notation for biracks that includes from the begining the
knowledege of the associated (or underlying, or derived) rack structure.
Motivated by results of Rump in the involutive case, this notation allows to
generalize some results from involutive case to the non necessarily involutive
solutions, and also to view some twisting constructions and its relation to the
underlying rack structure in a more transparent way. Two applications are
given.
