Auslander-Reiten components over pure-semisimple hereditary rings

被引：7

作者：

Angeleri Hugel, Lidia ^{[2
]}

Herbera, Dolors ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Verona, Dipartimento Informat Settore Matemat, I-37134 Verona, Italy

来源：

JOURNAL OF ALGEBRA | 2011年 / 331卷 / 01期

关键词：

Pure-semisimple rings; Pure-Semisimplicity Conjecture; Auslander-Reiten Theory; Tilting equivalence; Cotilting duality; ARTIN PROBLEM; MODULES; DECOMPOSITIONS; EXTENSIONS; EXISTENCE;

D O I：

10.1016/j.jalgebra.2010.10.039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Hugel (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. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：285 / 303

页数：19

共 31 条

[1] Finitely cotilting modules
Angeleri Hugel, L
[J]. COMMUNICATIONS IN ALGEBRA, 2000, 28 (04) : 2147 - 2172
[2] Assem I., 2006, Elements of Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory, V1
[3] AUSLANDER M., 1978, Lecture Notes in Pure Appl. Math., V37, P1
[4] Auslander M., 1976, Algebra, Topology and Category Theory, P1
[5] Auslander M., 1974, Commun. Algebra, V1, P177
[6] Auslander M., 1997, CAMBRIDGE STUD ADV M, V36
[7] BRUNE H, 1979, COMM ALGEBRA, V17
[8] TILTING, COTILTING, AND SERIALLY TILTED RINGS
COLBY, RR
FULLER, KR
[J]. COMMUNICATIONS IN ALGEBRA, 1990, 18 (05) : 1585 - 1615
[9] COLBY RR, 2004, CAMBRIDGE TRACTS MAT, V161
[10] ON THE STRUCTURE OF ASTERISK-MODULES
COLPI, R
MENINI, C
[J]. JOURNAL OF ALGEBRA, 1993, 158 (02) : 400 - 419

← 1 2 3 4 →