Construction of a quotient ring of Z2 F in which a binomial 1+w is invertible using small cancellation methods

We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring Z(2) F/I where Z(2) F is the group algebra of the free group F over the field Z(2), and the ideal I is generated by a single trinomial 1 + v + vw, where v is a complicated word depending on w. In Z(2) F/I we have (1 + w)-1 = v, so 1+ w becomes invertible. We construct an explicit linear basis of Z(2) F/I (thus showing that Z(2) F/I not equal 0). This is the first step in constructing rings with exotic properties.