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 …

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 …

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] …

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 …

The main results in this paper relate the concepts of flatness and projectiveness for finitely
generated ideals in a commutative ring with unity. In this discussion the idea of a …

It is proved that all modules over an integral domain have strongly flat cover if and only if
every flat-module is strongly flat. The domains satisfying this property are characterized by …

Recently,]~. DE ROBERT has considered the dual concepts of relative projectivity and
relative injectivity that extend the notions of quasi-projective and quasi-injective modules …

The mono-epi (ME) exact structure on the morphisms of an exact category is introduced and
used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and …

It is well-known that if R is a Noetherian ring or a local ring, then every finitely generated flat
R-module is projective (cf.(1),(3), R need not be commutative.). It is also known that if R is a …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …