ABSTRACT

Throughout this paper we will assume that all rings are commutative rings with identity, that ring homomorphisms preserve identities, and that a ring and its subrings have the same identity. In the second section of this paper we list some results which will be used in the sequel. We then consider some of the constructions and results of classical algebraic number theory in the context of the infinite Galois theory of rings. Most of the constructions and results in this second section either have appeared in the literature or are modifications of classical results.