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.

Let $(R,𝔪)$ be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated $R$-module.

Let $R$ be a commutative ring and $𝒞$ a semidualizing $R$-module. We investigate the relations between $𝒞$-flat modules and $𝒞$-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.

We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...

Let $f:A\to B$ and $g:A\to C$ be two ring homomorphisms and let $J$ and $J^{\text{'}}$ be ideals of $B$ and $C$, respectively, such that $f^{-1}\left(J\right)=g^{-1}\left(J^{\text{'}}\right)$. In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of $A$ with $(B,C)$ along $(J,J^{\text{'}})$ with respect to $(f,g)$ (denoted by $A{\bowtie }^{f,g}(J,J^{\text{'}})),$ introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.

We study whether the projective and injective properties of left $R$-modules can be implied to the special kind of left $R\left[x\right]$-modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.

Quasi-injective modules over valuation domains are classified by means of complete sets of cardinal invariants.

In this paper, we study the existence of the $n$-flat preenvelope and the $n$-FP-injective cover. We also characterize $n$-coherent rings in terms of the $n$-FP-injective and $n$-flat modules.