If is a prime number, then the ideal of factors uniquely as a product , where the are maximal ideals of . We may imagine the decomposition of into prime ideals geometrically as the fiber , where the exponents are the multiplicities of the fibers. Notice that the elements of are the prime ideals of that contain , i.e., the primes that divide . This chapter is about how to compute the and .
William Stein 2012-09-24