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Abelian group pairs having a trivial coGalois group

Paul Hill (2008)

Czechoslovak Mathematical Journal

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 = , 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.

Algebraic characterization of finite (branched) coverings

M. Mulero (1998)

Fundamenta Mathematicae

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...

Algebraic properties of rings of continuous functions

M. Mulero (1996)

Fundamenta Mathematicae

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.

Almost perfect domains

S. Bazzoni, L. Salce (2003)

Colloquium Mathematicae

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.

Bounds on Bass numbers and their dual

Abolfazl Tehranian, Siamak Yassemi (2007)

Archivum Mathematicum

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.

Flatness testing over singular bases

Janusz Adamus, Hadi Seyedinejad (2013)

Annales Polonici Mathematici

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),...

Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou, Moutu Abdou Salam Moutui (2020)

Czechoslovak Mathematical Journal

Let f : A B and g : A C be two ring homomorphisms and let J and J ' be ideals of B and C , respectively, such that f - 1 ( J ) = g - 1 ( J ' ) . 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 ' ) with respect to ( f , g ) (denoted by A f , g ( J , J ' ) ) , 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.

Injective and projective properties of R [ x ] -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

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

n -flat and n -FP-injective modules

Xiao Yan Yang, Zhongkui Liu (2011)

Czechoslovak Mathematical Journal

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.

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