 Corresponding to the Bézout property we may, in any commutative ring, consider the collection of elements of the form "pa" + "qb", where and range over the ring.This is the ideal generated by and , and is denoted simply ("a", "b").In a ring all of whose ideals are principal (a principal ideal domain or PID), this ideal will be identical with the set of multiples of some ring element "d"; then this is a greatest common divisor of and "b".