Torsion-free and mixed abelian groups

Abstract

If p is prime in I, we my form Ip, the ring of quotients of I with respect to (p). This is the ring of p-adic fractions consisting of ll elements of Q whose denominators re prime to p. Observe that p is the unique (up to ssocites) prime in the ring Ip. We must lso consider (unitary) modules over I,. The definitions given bove for groups my be pplied to Imodules, with the following simplification. Since I hs only one prime, we spek of the height of n element x, h(x), instead of the vrious p-heights.