Covers and Directed Colimits Page 1 Algebr Represent Theor (2006) 9: 423–430 DOI
10.1007/s10468-006-9030-5 Covers and Directed Colimits Robert El Bashir Received: 1 …

Throughout, all rings R are associative with identity, and all inodules are unitary right R-
modules. By a class K of modules we inean K is a collection of nlodules such that K is closed …

This paper continues the study of the existence of torsion-free covers with respect to a
faithful hereditary torsion theory (ℑ, F) of left modules over a ring R with unity. If the filter of …

Let A and B be two rings, M be a left B, right A bimodule and be the formal triangular matrix
ring. It is known that the category of right T-modules is equivalent to the category Ω of triples …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

We always let R denote a ring with identity element. All modules will be unital left R-
modules. We use IXI to denote the cardinality of a set X. If A is a set and Ma (aeA) are …

868 MARTINEZ HERNANDEZ where F'is a flat and F-divisible module, can be completed
commutatively. b) The diagram can be completed only by means of autornorphisms of F. In …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

Free ideal rings (FIRs) introduced in (4) form a natural generalization of principal ideal
domains (PIDs), to which they reduce in the commutative case. However, they include many …