The theory of rings of quotients has its origin in the work of 0. Ore and K. Asano
on the construction of the total ring of fractions, in the 1930's and 40's. But the
subject did not really develop until the end of the 1950's, when a number of
s appeared (by R.E. Johnson, Y. Utumi, A.W. Goldie, P. Gabriel,
J. Lambek, and others). Since then the progress has been rapid, and the subject
has by now attained a stage of maturity, where it is possible to make a systematic
account of it (which is the purpose of this book).