Let $ T $ be a complete local domain containing the integers with maximal ideal $ M $ such
that $| T/M| $ is at least the cardinality of the real numbers. Let $ p $ be a nonmaximal prime …

THE UNIFORM CLOSURE OF RATIONAL MODULES Page 1 THE UNIFORM CLOSURE OF
RATIONAL MODULES TAVAN T. TRENT AND JAMES L. WANG ABSTRACT For a smooth …

This is essentially an expository paper about m-primary ideals I in a local ring (R, m) which
have a single exceptional prime, ie, whose closed fiber in the normalization R\left (I\right) of …

In this note all rings considered are associative with an identity element 1 and all modules
are unital left modules. It is shown that a commutative ring $ R $ has principal ideals …

It is our purpose in this paper to investigate the relationship between two classes of ideals in
regular local rings R: prime ideals P such that R/P is factorial, and prime ideals Q which are …

Let i? be a commutative ring, let X an indeterminate, let Q be a prime ideal of R [X], and let
P= QD R. If Q= P [X], then Q is called an extended prime; otherwise, Q is called an upper to …

Introduction. The problem considered is a special case of the general problem of the extent
to which a module (F, A) is determined by its endomorphism ring E (F, A). We restrict our …

Let R be an integrally closed domain with quotient field K and θ be an element of an integral
domain containing R with θ integral over R. Let F (x) be the minimal polynomial of θ over K …

In this note we shall consider rings A with the property that any flat and finitely generated A-
module is projective, and we will prove that this class of rings is rather big. If we require that …

Let R and S be commutative rings with S an R-algebra. We say that R has descent with
respect to S provided the following condition is satisfied: If E is an R-module such that E@ a …