CYCLE-FINITE ALGEBRAS WITH ALMOST ALL INDECOMPOSABLE MODULES OF PROJECTIVE OR INJECTIVE DIMENSION AT MOST ONE

被引：10

作者：

Skowyrski, Adam ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

COLLOQUIUM MATHEMATICUM | 2013年 / 132卷 / 02期

关键词：

cycle-finite algebra; tame quasitilted algebra; generalized double tilted algebra; Auslander-Reiten quiver; projective dimension; injective dimension; AUSLANDER-REITEN COMPONENTS; CATEGORIES;

D O I：

10.4064/cm132-2-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.

引用

页码：239 / 270

页数：32

共 18 条

[1] Cycle-finite algebras having finitely many indecomposable modules lying on short paths with injective source and projective target
Skowyrski, Adam
JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (01) : 364 - 381
[2] CYCLE-FINITE ALGEBRAS WITH FINITELY MANY τ-RIGID INDECOMPOSABLE MODULES
Malicki, Piotr
Skowronski, Andrzej
COMMUNICATIONS IN ALGEBRA, 2016, 44 (05) : 2048 - 2057
[3] EXISTENCE OF CYCLE-FINITE ALGEBRAS OF INFINITE REPRESENTATION TYPE WITHOUT DIRECTING PROJECTIVE OR INJECTIVE MODULES
Malicki, Piotr
Antonio de la Pena, Jose
Skowronski, Andrzej
COLLOQUIUM MATHEMATICUM, 2017, 148 (02) : 165 - 190
[4] INJECTIVE MODULES WITH RESPECT TO MODULES OF PROJECTIVE DIMENSION AT MOST ONE
Bouchiba, Samir
El-Arabi, Mouhssine
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2019, 26 : 53 - 75
[5] The Krull-Gabriel Dimension of Cycle-Finite Artin Algebras
Skowronski, Andrzej
ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (01) : 215 - 233
[6] The Krull-Gabriel Dimension of Cycle-Finite Artin Algebras
Andrzej Skowroński
Algebras and Representation Theory, 2016, 19 : 215 - 233
[7] RESOLUTIONS BY GORENSTEIN INJECTIVE AND PROJECTIVE-MODULES AND MODULES OF FINITE INJECTIVE DIMENSION OVER GORENSTEIN RINGS
ENOCHS, EE
JENDA, OMG
COMMUNICATIONS IN ALGEBRA, 1995, 23 (03) : 869 - 877
[8] Modules of finite projective dimension for standardly stratified algebras
Platzeck, MI
Reiten, I
COMMUNICATIONS IN ALGEBRA, 2001, 29 (03) : 973 - 986
[9] WEAK-INJECTIVE MODULES OF WEAK DIMENSION AT MOST ONE
Lee, Sang Bum
COMMUNICATIONS IN ALGEBRA, 2011, 39 (11) : 4420 - 4427
[10] Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras
Antonio Lopez-Ramos, Juan
ARKIV FOR MATEMATIK, 2008, 46 (02): : 349 - 361

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