Primitivity of group rings of non-elementary torsion-free hyperbolic groups

被引：1

作者：

Solie, Brent B. ^{[1
]}

机构：

[1] Embry Riddle Aeronaut Univ, Dept Math, 3700 Willow Creek Rd, Prescott, AZ 86301 USA

来源：

JOURNAL OF ALGEBRA | 2018年 / 493卷

关键词：

Primitive group rings; Hyperbolic groups;

D O I：

10.1016/j.jalgebra.2017.09.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use a recent result of Alexander and Nishinaka to show that if G is a non-elementary torsion-free hyperbolic group and R is a countable domain, then the group ring RG is primitive. This implies that the group ring KG of any non-elementary torsion-free hyperbolic group G over a field K is primitive. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：438 / 443

页数：6

共 13 条

[1] Non-noetherian groups and primitivity of their group algebras [J].

Alexander, James ;

Nishinaka, Tsunekazu .

JOURNAL OF ALGEBRA, 2017, 473 :221-246

[2]

ALONSO J. M., 1990, GROUP THEORY GEOMETR, P3

[3]

[Anonymous], 1993, INT J ALGEBRA COMPUT

[4]

[Anonymous], 1992, International Journal of Algebra and Computation

[5]

[Anonymous], 1987, ESSAYS GROUP THEORY, DOI 10.1007/978-1-4613-9586-7_3

[6]

BAUMSLAG B, 1967, P LOND MATH SOC, V17, P402

[7] PRIMITIVE NOETHERIAN GROUP RINGS [J].

FARKAS, DR ;

PASSMAN, DS .

COMMUNICATIONS IN ALGEBRA, 1978, 6 (03) :301-315

[8]

Ghys E., 1990, PROGR MATH, V83, P165

[9]

Kharlampovich O., 2009, ARXIV09042423V3MATHG

[10]

PASSMAN DS, 1977, PURE APPL MATH

← 1 2 →