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 …

ON THE INJECTIVITY AND FLATNESS OF CERTAIN CYCLIC MODULES Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 48, Number 1, March …

When every finitely generated flat module is projective Page 1 Journal of Algebra 277 (2004)
542–558 www.elsevier.com/locate/jalgebra When every finitely generated flat module is …

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 shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …

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 …

A module is serial if its submodules are linearly ordered with respect to inclusion. A ring R is
called left serial if RR is a direct sum of serial modules, and R is called serial if it is both left …

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 …

1. Introduction, In this paper we prove several theorems about rings having a generous
supply of projective injective modules. This is a curious class of rings. For instance, every …

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 …