ABSTRACT
Ideals play the same role in a ring that normal subgroups play in a group; they arise as kernels of homomorphisms and allow the construction of quotient structures. Quite often one is in the situation that a certain ideal in a ring consists of elements which are “uninteresting” with respect to a certain question; in this case, one factorizes the ring modulo this ideal (modulo the “uninteresting” objects) and does only the essential computations. A special case of this procedure was already encountered in section 1, where we passed from calculations in ℤ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136554/b1e97aa6-f63a-4d22-960d-a98dde0e94f9/content/eq848.tif"/> to calculations in the residue-class rings ℤ n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136554/b1e97aa6-f63a-4d22-960d-a98dde0e94f9/content/eq849.tif"/> .
