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

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Steinberg, Benjamin¹ 

[1] CUNY City Coll, Dept Math, Convent Ave & 138th St, New York, NY 10031 USA

关键词: Etale groupoids;    Inverse semigroups;    Groupoid algebras;    Leavitt path algebras;    Prime rings;   

DOI  :  10.1016/j.jpaa.2018.09.003

来源: Elsevier

【 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.

【 授权许可】

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