Torsion-free covers are considered for objects in the category $q_2.$ Objects in the category $q_2$ are just maps in $R$-Mod. For $R=\mathbb{Z},$ we find necessary and sufficient conditions for the coGalois group $G(A⟶B),$ associated to a torsion-free cover, to be trivial for an object $A⟶B$ in $q_2.$ Our results generalize those of E. Enochs and J. Rado for abelian groups.

In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.

In the article appeared in this same journal, vol. 33, 1 (1989) pp. 85-97, some statements in the proof of Example 3.4B got scrambled.

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism...

This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.

Commutative rings all of whose quotients over non-zero ideals are perfect rings are called almost perfect. Revisiting a paper by J. R. Smith on local domains with TTN, some basic results on these domains and their modules are obtained. Various examples of local almost perfect domains with different features are exhibited.