Let R be an integral domain in which all finitely generated ideals are principal. Let M be a
projective R-module. It is well known that if M is finitely generated it is free. By a familiar …

1. Introduction. It is a well-known and basic result of homological alge-bra that the direct
product of an arbitrary family of injective modules over any ring is again injective [3, p. 8] …

The object of this paper is to study the relationship between certain projective modules and
their endomorphism rings. Specifically, the basic problem is to describe the projective …

Let R be a regular local ring with field of quotients K, let L be a finite separable field
extension of K and S the localization of the integral closure of R in L at some maximal ideal …

Introduction. The aim of this paper is to study conditions which reflect the projectivity of a
given finitely generated flat module over a commutative ring. The use of the invariant factors …

LET A. he a noetherian local ring and t an indeterminate over A. In (1) it is shown that when
A is regular of dimension 1, the finitely generated projective A [£]-modules are free. We show …

Introduction. Serre has asked [5, p. 243] whether projective modules over the polynomial
ring K [XI,***, X"], K a field, are free, and Seshadri has proved that this is so when n= 2. More …

In this paper we prove that all finitely generated projective modules over a polynomial ring k
[T~..... T,] are free when k is a field, or more generally a principal ideal domain. This settles …

More precisely, cll n R-module P uniformly-big, where b is n infinite crdinl, if (i) P cn be
generated by b elements, nd (ii) PlOP requires generators for ll two-sided ideals R). A free …

We start by considering the following three problems for a right R-module M= MR where R is
an associative ring with 1:(1) Characterize the modules M with the following property …