Generalized Subrings Of Arithmetic Rings

摘要

The generalized subrings of F_q are classified, the generalized subrings of Z/p~2 are investigated, and their complete classification is obtained for p = 2. Examples of F_∞-similar generalized fields, a computation of F_∞~(directX n), a description of cofinite subrings of Z_p, and examples of subrings of Z_∞ are given. A conjecture concerning cofinite subrings of Z is proposed, and some evidence for it is presented. Bibliography: 4 titles.