A characterization of graded von Neumann regular rings with applications to Leavitt path algebras

JOURNAL OF ALGEBRA

卷:567

Article

Lannstrom, Daniel¹ 

[1] Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden

关键词: Epsilon-strongly graded ring;    Von Neumann regular ring;    Leavitt path algebra;    Corner skew Laurent polynomial ring;    Partial crossed product;   

DOI  :  10.1016/j.jalgebra.2020.09.022

来源: Elsevier

【 摘 要 】

We prove a new characterization of graded von Neumann regular rings involving the recently introduced class of nearly epsilon-strongly graded rings. As our main application, we generalize Hazrat's result that Leavitt path algebras over fields are graded von Neumann regular. More precisely, we show that a Leavitt path algebra L-R(E) with coefficients in a unital ring R is graded von Neumann regular if and only if R is von Neumann regular. We also prove that both Leavitt path algebras and corner skew Laurent polynomial rings over von Neumann regular rings are semiprimitive and semiprime. Thereby, we generalize a result by Abrams and Aranda Pino on the semiprimitivity of Leavitt path algebras over fields. (C) 2020 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free