 multiplicative inverses are added to the ring.Concretely, if "S" is a multiplicatively closed subset of "R" (i.e.whenever then so is "st") then the "localization" of "R" at "S", or "ring of fractions" with denominators in "S", usually denoted "S"−1"R" consists of symbols
subject to certain rules that mimic the cancellation familiar from rational numbers.