0. Introduction. Let<€ be the category of commutative rings with unit, and regard Spec (as in
[1]) as a contra variant functor from# to 3~, the category of topological spaces and …

Throughout this paper the term ring will denote a commutative ring with unity and the term
integral domain will denote a ring having no nonzero divisors of zero. The set of all prime …

1. Introduction. The paper consists of two sections which may, for the most part, be read
independently. Part I is devoted mainily to the study of compact rings. We first give some …

The most important part of this paper is contained in? IV, where is defined a notion of"
multiplicity"(which might also have been called degree of ramification) in a complete local …

1. Introduction. The concept of prime ideal has played an important role in the theory of
commutative rings, but has not been used so extensively in the study of noncommutative …

Introduction. The concept of a local ring was introduced by Krull [7]('), who defined such a
ring as a commutative ring 9D in which every ideal has a finite basis and in which the set m …

For the simplest manifestation of this role, consider the compact space N* obtained from the
discrete space of positive integers N by adjoining a single point, o. In the ring C (N*) of all …

0. Introduction. Let R and R denote commutative rings with identity. A radical ideal of R is an
intersection of prime ideals, and a J-radical ideal is an intersection of maximal ideals. If R …

The generalization studied here is that instead of merely one norm defined on A there is a
family of them, each satisfying 1.1; but of course it is natural to permit\\x\\= 0 even though xf …

We also construct an F-ring that is not an Hermite ring, and an Hermite ring that is not an
elementary divisor ring. To produce these examples, we translate the algebraic conditions …