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<p>In this paper, we describe the behavior of Lie <i>n</i>-centralizers acting on the specific subsets within unital prime rings of characteristic not 2. Subsequently, we employ these findings to characterize generalized Lie <i>n</i>-derivations on such rings. Our results extend previous research on standard operator algebras on Banach spaces and von Neumann factors. Moreover, we introduce characterizations for generalized Lie <i>n</i>-derivations at local products when restricted to factor von Neumann algebras. As an application of the obtained results, we present some variants of Posner’s second theorem on prime rings.</p>

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Structure of Lie Centralizer-like Mappings on Prime Rings and their Applications

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Behrooz Fadaee,
  • Hoger Ghahramani

摘要

In this paper, we describe the behavior of Lie n-centralizers acting on the specific subsets within unital prime rings of characteristic not 2. Subsequently, we employ these findings to characterize generalized Lie n-derivations on such rings. Our results extend previous research on standard operator algebras on Banach spaces and von Neumann factors. Moreover, we introduce characterizations for generalized Lie n-derivations at local products when restricted to factor von Neumann algebras. As an application of the obtained results, we present some variants of Posner’s second theorem on prime rings.