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Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring and let C be a semidualizing R -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every G C -injective module G , the character module G + is G C -flat, then the class 𝒢ℐ C ( R ) ∩ 𝒜 C ( R ) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class 𝒢ℐ C ( R ) ∩ 𝒜 C ( R ) is covering....

Relative hermitian Morita theory. Part II: Hermitian Morita contexts.

Pieter Verhaeghe, Alain Verschoren (1992)

Publicacions Matemàtiques

We introduce the notion of a relative hermitian Morita context between torsion triples and we show how these induce equivalences between suitable quotient categories of left and right modules.Due to the lack of involutive bimodules, the induced Morita equivalences are not necessarily hermitian, however.

Relative subanalytic sheaves

Teresa Monteiro Fernandes, Luca Prelli (2014)

Fundamenta Mathematicae

Given a real analytic manifold Y, denote by Y s a the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor ℱ ↦ ℱ S on the category of sheaves on Y s a and study its properties. Roughly speaking, ℱ S is a sheaf on X s a × S . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.

Relative theory in subcategories

Soud Khalifa Mohamed (2009)

Colloquium Mathematicae

We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].

Relative weak derived functors

Panneerselvam Prabakaran (2020)

Commentationes Mathematicae Universitatis Carolinae

Let R be a ring, n a fixed non-negative integer, 𝒲 ℐ the class of all left R -modules with weak injective dimension at most n , and 𝒲 ℱ the class of all right R -modules with weak flat dimension at most n . Using left (right) 𝒲 ℐ -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that - ⊗ - is right balanced on ℳ R × R ℳ by 𝒲 ℱ × 𝒲 ℐ , and investigate the global right 𝒲 ℐ -dimension of R ℳ by right derived functors of ⊗ .

Relatively exact modules

Ladislav Bican (2003)

Commentationes Mathematicae Universitatis Carolinae

Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice ℰ τ ( M ) of submodules of a torsionfree module M consisting of all submodules N of M such that M / N is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of M / N is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application...

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