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.
引用
收藏
页码：2474 / 2488
页数：15
相关论文
共 50 条
  • [21] Leavitt path algebras of quantum quivers
    Graham, Joshua
    Goswami, Rishabh
    Palin, Jason
    ARCHIV DER MATHEMATIK, 2025, 124 (01) : 29 - 48
  • [22] On the Ideals of Ultragraph Leavitt Path Algebras
    T. T. H. Duyen
    D. Gonçalves
    T. G. Nam
    Algebras and Representation Theory, 2024, 27 : 77 - 113
  • [23] Lie solvable Leavitt path algebras
    Tran Giang Nam
    Zhang, Zerui
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (10)
  • [24] On graded primitive Leavitt path algebras
    Rangaswamy, Kulumani M.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (09)
  • [25] Ideals of etale groupoid algebras and Exel's Effros-Hahn conjecture
    Steinberg, Benjamin
    JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2021, 15 (03) : 829 - 839
  • [26] Homotopy classification of Leavitt path algebras
    Cortinas, Guillermo
    Montero, Diego
    ADVANCES IN MATHEMATICS, 2020, 362
  • [27] On the Ideals of Ultragraph Leavitt Path Algebras
    Duyen, T. T. H.
    Goncalves, D.
    Nam, T. G.
    ALGEBRAS AND REPRESENTATION THEORY, 2024, 27 (01) : 77 - 113
  • [28] On inverse semigroup C*-algebras and crossed products
    Milan, David
    Steinberg, Benjamin
    GROUPS GEOMETRY AND DYNAMICS, 2014, 8 (02) : 485 - 512
  • [29] Leavitt Path Algebras in Which Every Lie Ideal is an Ideal and Applications
    Khanh, Huynh Viet
    TRANSFORMATION GROUPS, 2024,
  • [30] Leavitt path algebras with bounded index of nilpotence
    Rangaswamy, Kulumani M.
    Srivastava, Ashish K.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2019, 18 (10)
12345