Auslander-Reiten components over pure-semisimple hereditary rings

Lidia Angeleri Hügel; Dolors Herbera

doi:10.1016/j.jalgebra.2010.10.039

Auslander-Reiten components over pure-semisimple hereditary rings

Lidia Angeleri Hügel, Dolors Herbera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri Hügel (2007) [2]. We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. © 2010 Elsevier Inc.

Original language	English
Pages (from-to)	285-303
Journal	Journal of Algebra
Volume	331
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2010.10.039
Publication status	Published - 1 Apr 2011

Keywords

Auslander-Reiten Theory
Cotilting duality
Pure-semisimple rings
Pure-Semisimplicity Conjecture
Tilting equivalence

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title = "Auslander-Reiten components over pure-semisimple hereditary rings",

abstract = "Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri H{\"u}gel (2007) [2]. We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. {\textcopyright} 2010 Elsevier Inc.",

keywords = "Auslander-Reiten Theory, Cotilting duality, Pure-semisimple rings, Pure-Semisimplicity Conjecture, Tilting equivalence",

author = "{Angeleri H{\"u}gel}, Lidia and Dolors Herbera",

year = "2011",

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doi = "10.1016/j.jalgebra.2010.10.039",

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T1 - Auslander-Reiten components over pure-semisimple hereditary rings

AU - Angeleri Hügel, Lidia

AU - Herbera, Dolors

PY - 2011/4/1

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N2 - Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri Hügel (2007) [2]. We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. © 2010 Elsevier Inc.

AB - Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting and cotilting module W studied in L. Angeleri Hügel (2007) [2]. We then apply the tilting and the cotilting functors to study the endomorphism ring of W and its Auslander-Reiten components. Finally, we transfer this information to the category of right R-modules. © 2010 Elsevier Inc.

KW - Auslander-Reiten Theory

KW - Cotilting duality

KW - Pure-semisimple rings

KW - Pure-Semisimplicity Conjecture

KW - Tilting equivalence

U2 - 10.1016/j.jalgebra.2010.10.039

DO - 10.1016/j.jalgebra.2010.10.039

M3 - Article

VL - 331

SP - 285

EP - 303

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -