Infinitely Generated Gorenstein Tilting Modules
Pooyan Moradifar,Siamak Yassemi +1 more
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TL;DR: Gorenstein tilting approximations as discussed by the authors have been used to study the existence of complements to partial Gorenstein tilts and their associated relative cotorsion pairs, as well as some connections between finitistic dimension conjectures.
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Abstract: The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, and infinitely generated relative tilting modules have recently been studied by many authors in the context of Gorenstein homological algebra. In this work, we build on the theory of infinitely generated Gorenstein tilting modules by developing “Gorenstein tilting approximations” and employing these approximations to study Gorenstein tilting classes and their associated relative cotorsion pairs. As applications of our results, we discuss the problem of existence of complements to partial Gorenstein tilting modules as well as some connections between Gorenstein tilting modules and finitistic dimension conjectures.
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Citations
Relation between balanced pairs and TTF triples
Weiqing Li
TL;DR: This paper explores the relationship between balanced pairs and TTF triples in abelian categories, establishing a bijection between their equivalence classes under certain conditions, and providing applications to ring theory and counterexamples to open questions.
The bongartz's theorem of gorenstein cosilting complexes
Hailou Yao,Qianqian Yuan +1 more
TL;DR: This paper introduces Gorenstein cosilting complexes and studies their properties, generalizing cosilting complexes in relative homological methods, and investigates the existence of a relative Bongartz's theorem with a constructed complement for Gorenstein precosilting complexes.
Gorenstein silting complexes
Weiqing Cao,Jiaqun Wei +1 more
TL;DR: In this article, the notion of Gorenstein silting complexes was introduced and studied, which is a generalization of the tilting modules in the context of a single-input single-output (SISO) configuration.
References
Triangulated Categories in the Representation of Finite Dimensional Algebras
Dieter Happel
- 11 Feb 1988
TL;DR: The use of triangulated categories in the study of representations of finite-dimensional algebras has been studied extensively in the literature as discussed by the authors, and triangulation is a useful tool in studying tilting processes.
1.9K
Finitistic dimension and a homological generalization of semi-primary rings
TL;DR: In this article, Kaplansky showed that a commutative ring R is left T-nilpotent if, given any sequence {at} of elements in N, there exists an re such that ai • • • an = 0.
Gorenstein homological dimensions
TL;DR: In this paper, the closely related Gorenstein projective, Goren stein injective and 2-at dimensions of modules are studied, and a generalization of these results is given to give homological descriptions of the GORNE dimensions over arbitrary associative rings.
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