Abstract :
Let T be an integral domain, I a nonzero proper ideal of T, and phi : T→T/I the natural projection. For an integral domain D which is a proper subring of T/I, R=phi−1(D) is then a subring of T. We investigate the class group Cl(R), the Picard group Pic(R), and the local class group G(R) of the pullback R.
