Sentence:  Perhaps it is an advantage of the "<WSD>associative</WSD> algebraic geometry" we have tried to develop in foregoing chapters that it is independent of braidings and further generalizations because it will remain valid as long as the corresponding "function"-rings constructed in these theories are <WSD>associative</WSD> algebras. 
Meaning of the word marked with <WSD> tags:  Such that, for any operands a, b and c, (a * b) * c = a * (b * c);  whose multiplication operation is associative.