The basic example is the completion of Z at the principal ideal ("p") generated by a prime number "p"; it is called the ring of "p"-adic integers and is denoted Z"p". The completion can in this case be constructed also from the "p"-adic absolute value on Q. The "p"-adic absolute value on Q is a map formula_197 from Q to R given by formula_198 where formula_199 denotes the exponent of "p" in the prime factorization of a nonzero integer "n" into prime numbers (we also put formula_200 and formula_201). It defines a distance function on Q and the completion of Q as a metric space is denoted by Q"p". It is again a field since the field operations extend to the completion. The subring of Q"p" consisting of elements "x" with formula_202 is isomorphic to Z"p".