Algorithm for computing the factor ring of an ideal in Dedekind domain   with finite rank
  We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial-time. We provide two applications of the algorithm: judging whether a given ideal is prime or prime power. The main algorithm is based on basis representation of finite rings which is computed via Hermite and Smith normal forms. 
Dandan Huang and Yingpu Deng
math.RA cs.SC