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   Articles with "auslander reiten" as a keyword



Simplicial structures in higher Auslander–Reiten theory

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recommendations! Published in 2019 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2019.106762

Abstract: Abstract We develop a novel combinatorial perspective on the higher Auslander algebras of type A , a family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This approach reveals interesting simplicial structures… read more here.

Keywords: reiten theory; simplicial structures; auslander reiten; auslander ... See more keywords
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Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories

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recommendations! Published in 2018 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2019.04.017

Abstract: Abstract We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt… read more here.

Keywords: reiten theory; auslander reiten; krull schmidt; schmidt categories ... See more keywords
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ON COMPONENTS OF STABLE AUSLANDER–REITEN QUIVERS THAT CONTAIN HELLER LATTICES: THE CASE OF TRUNCATED POLYNOMIAL RINGS – CORRIGENDUM

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recommendations! Published in 2019 at "Nagoya Mathematical Journal"

DOI: 10.1017/nmj.2018.51

Abstract: The original publication of [AKM] contained several errors that the authors wish to correct in the following. Throughout, O will be a complete discrete valuation ring, and A will be a symmetric O-order (refer to… read more here.

Keywords: contain heller; auslander reiten; lattices case; stable auslander ... See more keywords
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Generalization of Auslander-Reiten duality for algebras

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recommendations! Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1922694

Abstract: Abstract Let R be a Cohen-Macaulay local ring of dimension d with canonical module ωR . In this article we extend Auslander-Reiten duality theorem to certain R-algebras. As a consequence of our argument, we obtain… read more here.

Keywords: generalization auslander; reiten duality; duality algebras; auslander reiten ... See more keywords
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Auslander-Reiten duality for Grothendieck abelian categories

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recommendations! Published in 2018 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/7379

Abstract: Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext^1(C,-) into… read more here.

Keywords: duality; grothendieck abelian; abelian categories; auslander reiten ... See more keywords

The generalized Auslander–Reiten duality on an exact category

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recommendations! Published in 2018 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498818502274

Abstract: We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–Schmidt exact category [Formula: see text]. This duality induces the generalized Auslander–Reiten translation functors [Formula: see text] and [Formula: see text]. They are mutually… read more here.

Keywords: auslander reiten; see text; formula see; generalized auslander ... See more keywords
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Integer sequences arising from Auslander–Reiten quivers of some hereditary artin algebras

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recommendations! Published in 2020 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498821500511

Abstract: Categorification of some integer sequences are obtained by enumerating the number of sections in the Auslander–Reiten quiver of algebras of finite representation type. read more here.

Keywords: quivers hereditary; reiten quivers; auslander reiten; arising auslander ... See more keywords

The existence of n-Auslander–Reiten sequences via determined morphisms

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recommendations! Published in 2021 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498823500317

Abstract: Let [Formula: see text] be a commutative artinian ring and [Formula: see text] a small Ext-finite Krull–Schmidt [Formula: see text]-abelian [Formula: see text]-category with enough projectives and injectives. We introduce two full subcategories [Formula: see… read more here.

Keywords: determined morphisms; auslander reiten; see text; formula see ... See more keywords