Strongly simply connected algebras with super-decomposable pure-injective modules

被引：2

作者：

Pastuszak, Grzegorz ^{[1
]}

机构：

[1] Polish Acad Sci, Ctr Theoret Phys, PL-02668 Warsaw, Poland

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2015年 / 219卷 / 08期

关键词：

KRULL-GABRIEL DIMENSION; TAME ALGEBRAS; MODEL-THEORY; TITS; FINITE; FORM;

D O I：

10.1016/j.jpaa.2014.10.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Assume that k is an algebraically closed field of characteristic different than 2 and A is a strongly simply connected k-algebra. We show that A is of non-domestic type if and only if the width of the lattice of all pointed A-modules is undefined. Hence it follows by a result of Ziegler that A admits a super-decomposable pure injective module if and only if A is of non-domestic type, if the base field k is countable. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：3314 / 3321

页数：8

共 38 条

[1]

[Anonymous], 2006, Techniques of Representation Theory, London Math. Soc. Student Texts

[2] Tame algebras and Tits quadratic forms [J].

Bruestle, Thomas ;

Antonio de la Pena, Jose ;

Skowronski, Andrzej .

ADVANCES IN MATHEMATICS, 2011, 226 (01) :887-951

[3]

CRAWLEYBOEVEY W, 1991, P LOND MATH SOC, V63, P241

[4] The Tits and Euler forms of a tame algebra [J].

de la Peña, JA ;

Skowronski, A .

MATHEMATISCHE ANNALEN, 1999, 315 (01) :37-59

[5]

de la Peña JA, 2014, T AM MATH SOC, V366, P395

[6] Geometric and homological characterizations of polynomial growth strongly simply connected algebras [J].

delaPena, JA ;

Skowronski, A .

INVENTIONES MATHEMATICAE, 1996, 126 (02) :287-296

[7]

Drozd Yu.A., 1979, Amer. Math. Soc. Transl., V128, P39

[8]

Gabriel P., 1981, LECT NOTES MATH, V903, P68

[9] THE KRULL-GABRIEL DIMENSION OF THE REPRESENTATION-THEORY OF A TAME HEREDITARY ARTIN ALGEBRA AND APPLICATIONS TO THE STRUCTURE OF EXACT SEQUENCES [J].

GEIGLE, W .

MANUSCRIPTA MATHEMATICA, 1985, 54 (1-2) :83-106

[10]

Harland R., 2011, THESIS U MANCHESTER

← 1 2 3 4 →