The localization is frequently applied to a commutative ring "R" with respect to the complement of a prime ideal (or a union of prime ideals) in "R". In that case formula_175, one often writes formula_176 for formula_177. formula_176 is then a local ring with the maximal ideal formula_179. This is the reason for the terminology "localization". The field of fractions of an integral domain "R" is the localization of "R" at the prime ideal zero. If formula_180 is a prime ideal of a commutative ring "R", then the field of fractions of formula_181 is the same as the residue field of the local ring formula_176 and is denoted by formula_183.