利维特路径代数的准巴儿 * * -环特性化

Pub Date : 2024-05-29 DOI:10.1134/s0037446624030145

M. Ahmadi, A. Moussavi

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引用次数: 0

摘要

我们说，如果对于 $ R $ 的每个分级理想 $ I $ ，$ I $ 的右湮没子是由一个同质偶等（投影）生成的，那么分级环（$ * $-环）就是一个分级准贝尔环（分级准贝尔 $ * $-环）。我们证明，当且仅当一个 Leavitt 路径代数是分级准 Baer（graded quasi-Baer $ * $）时，它才是准 Baer（quasi-Baer $ * $）。我们证明，如果一个 Leavitt 路径代数的零成分是准 Baer（quasi-Baer $ * $），那么这个 Leavitt 路径代数就是准 Baer（quasi-Baer $ * $）。然而，我们给出了一些例子，表明反向蕴涵是失败的。最后，我们从底层图的性质出发，描述了准 Baer $ * $-环的 Leavitt 路径代数的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Quasi-Baer $ * $ -Ring Characterization of Leavitt Path Algebras

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Quasi-Baer $ * $ -Ring Characterization of Leavitt Path Algebras

We say that a graded ring ($ * $-ring) $ R $ is a graded quasi-Baer ring (graded quasi-Baer $ * $-ring) if, for each graded ideal $ I $ of $ R $, the right annihilator of $ I $ is generated by a homogeneous idempotent (projection). We prove that a Leavitt path algebra is quasi-Baer (quasi-Baer $ * $) if and only if it is graded quasi-Baer (graded quasi-Baer $ * $). We show that a Leavitt path algebra is quasi-Baer (quasi-Baer $ * $) if its zero component is quasi-Baer (quasi-Baer $ * $). However, we give some example that showing that the converse implication fails. Finally, we characterize the Leavitt path algebras that are quasi-Baer $ * $-rings in terms of the properties of the underlying graph.

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