Any maximal ideal is a prime ideal or, more briefly, is prime. Moreover, an ideal "formula_137" is prime if and only if the factor ring "formula_138" / "formula_137" is an integral domain. Proving that an ideal is prime, or equivalently that a ring has no zero-divisors can be very difficult. Yet another way of expressing the same is to say that the complement "formula_140" is multiplicatively closed. The localisation "formula_141"("R" \ "p")−1"R" is important enough to have its own notation: "formula_142". This ring has only one maximal ideal, namely "formula_143". Such rings are called local.