Every projective module is flat. Conversely, every flat module is a direct limit of finitely
generated free modules; this was proved independently by Govorov and Lazard in the …

Let C be a class of modules and L= lim→ C the class of all direct limits of modules from C.
The class L is well understood when C consists of finitely presented modules: L then enjoys …

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 …

Although it is not. true that the section functor r'a with support in the variety of the ideal a
takes a bounded complex of flat modules into a bounded complex of flat modules, a …

En 1958, Kaplansky [6] inaugura l'etude des modules projectifs de type infini en montrant
qu'ils sont somme directe de modules de type denombrable, et qu'ils sont libres sur les …

The purpose of this expository note is to establish the fact mentioned in the title. While this is
not difficult and requires no new ideas, it seems worth doing, as such a simple …

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 …

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 …

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 …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …