p-adic Integer

A -adic integer is a p-adic number of the form , where ,  are integers, and  is prime. It is sufficient to take  in the set .

Equivalently, a -adic integer is an element of the inverse limit of the rings  for .

The same ring is obtained by taking the  to be any rationals with denominator coprime to .

REFERENCES:

Cassels, J. W. S. Ch. 2 in Lectures on Elliptic Curves. New York: Cambridge University Press, 1991.