Prime etale groupoid algebras with applications to inverse semigroup and Leavitt path algebras

被引：11
|
作者：
Steinberg, Benjamin [1 ]
机构：
[1] CUNY City Coll, Dept Math, Convent Ave & 138th St, New York, NY 10031 USA
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2019年 / 223卷 / 06期
关键词：
Etale groupoids; Inverse semigroups; Groupoid algebras; Leavitt path algebras; Prime rings; STEINBERG ALGEBRAS; SEMIPRIMITIVITY; SIMPLICITY;
D O I：
10.1016/j.jpaa.2018.09.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we give some sufficient and some necessary conditions for an etale groupoid algebra to be a prime ring. As an application we recover the known primeness results for inverse semigroup algebras and Leavitt path algebras. It turns out that primeness of the algebra is connected with the dynamical property of topological transitivity of the groupoid. We obtain analogous results for semiprimeness. (C) 2018 Elsevier B.V. All rights reserved.
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页码：2474 / 2488
页数：15
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