Approximations and Endomorphism Algebras of Modules

By R. Göbel, Jan Trlifaj. 2006

654 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c8485481a1c2b62c8007bd397c77b81e51e2f787

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In Algebra and Number Theory

Citations in the corpus

The Tilting–Cotilting Correspondence (2017, background): “The following definitions are standard; see for instance [79], [82, §5] or [71, §§3 and 4] and the references there (the concept of a cotorsion pair goes back to [77] and have been extensively used in representation and module theory [48, 38]).”
On exact categories and applications to triangulated adjoints and model structures (2010, methodology): “For instance, [21] deals with modules while the papers mentioned before would preferably need the corresponding theory at least for Grothendieck categories.”
Homotopy Equivalences induced by Balanced Pairs (2008, background): “The cotorsion pair (X , Y) is said to be complete provided that for each M ∈ A there exist short exact sequences 0 → Y → X → M → 0 and 0 → M → Y ′ → X ′ → 0 with X, X ′ ∈ X and Y , Y ′ ∈ Y ([12, Chapter 7] and [20,14,9]).”
Almost free modules and Mittag-Leffler conditions (2009, background): “ed free modules is called a κ–free abelian group. This class of groups as well as their module theoretic counterpart, the κ-free modules, have been studied in detail [10, Chaps. IV and VII], see also [21]. A natural extension of these concepts to modules over non–hereditary is the following (cf. [10”
Mittag-Leffler conditions on modules (2007, background): “1This terminology differs from previous use, cf.[25].”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, background): “There is, however, another important aspect—the model theoretic approach links the theory of triangulated categories to approximation theory [32], allowing deep insights on both sides.”
Gorenstein Homological Algebra of Artin Algebras (2017, neutral): “Applying the condition (C3) to M ′ we (2)The cotorsion pair introduced here is also referred as a complete cotorsion pair; see [28, 32].”
Cosilting Modules (2015, methodology): “We refer to [13] for other notions and notations used in this paper.”