We give a proof, based on the analysis of the divisible envelopes of flat modules, of the fact
that an integral domain R is almost perfect if and only if all divisible R-modules are weak …

We show that a weak-injective module over an integral domain need not be pure-injective
(Theorem 2.3). Equivalently, a torsion-free Enochs-cotorsion module over an integral …

Let R be a commutative integral domain with 1 and Q its field of quotients. We show that if pd
$\sb {\rm R} $ Q= 1, then Q/R is a direct sum of countably generated R-modules. We also …

Over integral domains, we characterize modules of finite weak dimension⩽ n in terms of h-
divisible pure-injective modules (Theorems 2.1 and 2.2). We compare various classes of h …

In the setting of Noetherian or Dedekind domains, we investigate the properties of very flat
and contraadjusted modules. These are the modules from the respective classes in the …

This note is devoted to the study of divisible modules over arbitrary commutative domains R
with 1. Whereas divisible modules over Dedekind domains can be completely characterized …

We consider a generalization of a problem raised by P. Griffith on abelian groups to modules
over integral domains, and prove an analogue of a theorem of M. Dugas and J. Irwin …

We consider the problem of characterizing the commutative domains such that every module
admits a divisible envelope or a-cover, where is the class of modules of projective …

We consider the perfect cotorsion pair (𝒫1, 𝒟) over a commutative ring (often over a domain)
R consisting of modules of projective dimension≤ 1 and of divisible modules, respectively …

The aim of this paper is to describe an equivalence between the full subcategory of Mod-R
whose objects are all the divisible modules over an integral domain R and a suitable full …