One of the aims of this paper is to answer the following question: Let R be a commutative
ring for which projective ideals are finitely generated; is the same valid in R [x], the …

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 …

We are concerned with a question of H. Bass and D. Quillen which asks whether the
following is true: If A is a regular noetherian ring, then every finitely generated projective …

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 …

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 …

A where Po is a projective module over A (see [2],[5] and [6]). If A is not normal it is known
that a projective module P over A [X] need not come from A (see for instance [2], p. 325) …

0. Introductory Remarks. A finitely generated projectiveA-module P is said to be cancellative
if whenever there is an isomorphism of P? Q and P'? Q, for some finitely generated …

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 …

A note on regular modules Page 1 BULL. AUSTRAL. MATH. SOC. I6A30 VOL. II ( 1 9 7 4 ) , 3 5
9 - 3 6 4 . ( I 6 A 5 O ) A note on regular modules VS Ramamurthi Kaplansky's observation …

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 …