We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

Several papers find conditions on a ring R in order for certain properties of modules to be
preserved under direct sums, and direct products. Thus we know when direct sums of …

We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

In this paper we show that if R is a ring of Krull dimension d and M is a strongly copure flat
(respectively, strongly copure injective) module, then E⊗ RM (respectively, HomR (E, M)) is …

Let R be an associative ring with identity. A right R-module M is called cotorsion if Ext"(F,
M)= 0 for every flat right R-module F. These modules were introduced by Harrison [21] in the …

n-FLAT AND n-FP-INJECTIVE MODULES 1. Introduction We use R-Mod (resp., Mod-R) to
denote the category of all left (resp., right) Page 1 Czechoslovak Mathematical Journal, 61 (136) …

We introduce nets in rings, which turn out to describe right flat modules and left flat modules
over a fixed ring R at the same time. As an application we prove that for a finitely generated …