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Rad-supplemented modules

Engin Büyükaşik, Engin Mermut, Salahattin Özdemir (2010)

Rendiconti del Seminario Matematico della Università di Padova

Rational fibrations in differential homological algebra.

Aniceto Murillo (1990)

Extracta Mathematicae

Realization of long exact sequences of abelian groups.

Irwin S. Pressman (1990)

Publicacions Matemàtiques

Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories...

Reedy categories which encode the notion of category actions

Julia E. Bergner, Philip Hackney (2015)

Fundamenta Mathematicae

We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...

Reflexive and dihedral (co)homology of a pre-additive category.

Gouda, Yasien Gh. (2001)

International Journal of Mathematics and Mathematical Sciences

Relative cohomolgy of groups.

N. Habegger, V. Jones, O.P. Ortiz (1984)

Commentarii mathematici Helvetici

Relative cyclic homology and the Bass conjecture.

James A. Schafer (1992)

Commentarii mathematici Helvetici

Relative derived functors and the homology of groups

Graham J. Ellis (1990)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Relative EXT groups of Abelian categories

Chaoling Huang, Kai Deng (2013)

Matematički Vesnik

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 ${𝒢ℐ}_{C} (R) \cap 𝒜_{C} (R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class ${𝒢ℐ}_{C} (R) \cap 𝒜_{C} (R)$ is covering....

Relative homological categories.

Janelidze, Tamar (2006)

Journal of Homotopy and Related Structures

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 $- \otimes -$ is right balanced on $ℳ_{R} \times_{R} ℳ$ by $𝒲 ℱ \times 𝒲 ℐ$ , and investigate the global right $𝒲 ℐ$ -dimension of $_{R} ℳ$ by right derived functors of $\otimes$ .

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