the mapping from rings of integers "r" to their corresponding class groups is functorial, and the class group can be subsumed under the heading of algebraic k-theory, with "k"("r") being the functor assigning to "r" its ideal class group; more precisely, "k"("r") = z×"c"("r"), where "c"("r") is the class group. higher k groups can also be employed and interpreted arithmetically in connection to rings of integers.