Largest Ideals in Leavitt Path Algebras

被引：2

作者：

Cam, Vural ^{[1
]}

Gil Canto, Cristobal ^{[2
]}

Kanuni, Muge ^{[3
]}

Siles Molina, Mercedes ^{[2
]}

机构：

[1] Selcuk Univ, Dept Math, TR-42003 Selcuklu Konya, Turkey

[2] Univ Malaga, Fac Ciencias, Dept Algebra Geometria & Topol, Campus Teatinos S-N, E-29071 Malaga, Spain

[3] Duzce Univ, Dept Math, TR-81620 Duzce, Turkey

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2020年 / 17卷 / 02期

关键词：

Leavitt path algebra; socle; extreme cycle; line point; purely infinite ideal; CYCLES; SOCLE;

D O I：

10.1007/s00009-020-1486-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We identify the largest ideals in Leavitt path algebras: the largest locally left/right artinian (which is the largest semisimple one), the largest locally left/right noetherian without minimal idempotents, the largest exchange, and the largest purely infinite. This last ideal is described as a direct sum of purely infinite simple pieces plus purely infinite non-simple and non-decomposable pieces. The invariance under ring isomorphisms of these ideals is also studied.

引用

页数：21

共 14 条

[1] The Leavitt path algebra of a graph
Abrams, G
Pino, GA
[J]. JOURNAL OF ALGEBRA, 2005, 293 (02) : 319 - 334
[2] Abrams G, 2017, LECT NOTES MATH
[3] Chain conditions for Leavitt path algebras
Abrams, Gene
Aranda Pino, Gonzalo
Perera, Francesc
Siles Molina, Mercedes
[J]. FORUM MATHEMATICUM, 2010, 22 (01) : 95 - 114
[4] Nonstable K-theory for graph algebras
Ara, P.
Moreno, M. A.
Pardo, E.
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2007, 10 (02) : 157 - 178
[5] Local rings of exchange rings
Ara, P
Lozano, MG
Molina, MS
[J]. COMMUNICATIONS IN ALGEBRA, 1998, 26 (12) : 4191 - 4205
[6] Extensions of exchange rings
Ara, P
[J]. JOURNAL OF ALGEBRA, 1997, 197 (02) : 409 - 423
[7] Pino AA, 2010, AM J MATH, V132, P563
[8] Cycles in Leavitt path algebras by means of idempotents
Aranda Pino, Gonzalo
Brox, Jose
Siles Molina, Mercedes
[J]. FORUM MATHEMATICUM, 2015, 27 (01) : 601 - 633
[9] Pino GA, 2010, REV MAT IBEROAM, V26, P611
[10] Using Steinberg algebras to study decomposability of Leavitt path algebras
Clark, Lisa Orloff
Barquero, Dolores Martin
Gonzalez, Cÿndido Martin
Molina, Mercedes Siles
[J]. FORUM MATHEMATICUM, 2017, 29 (06) : 1311 - 1324

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