 If formula_187 is a prime ideal of a commutative ring "R", then the field of fractions of formula_188 is the same as the residue field of the local ring formula_183 and is denoted by formula_190.If "M" is a left "R"-module, then the localization of "M" with respect to "S" is given by a change of rings formula_191.The most important properties of localization are the following