DM-GAA

Article in press

Authors:

A. Khotanloo

Ali Khotanloo

Faculty of Mathematics Sciences and Statistics
Malayer University
P.O. Box 6517-95863, Malayer, Iran

email: alikhotanloo@yahoo.com

Sh. Goodarzi

Sh. Goodarzi

Faculty of Mathematics Sciences and Statistics
Malayer University
P.O. Box 6517-95863, Malayer, Iran

email: shima.goodarzi@stu.malayeru.ac.ir

Title:

The structure of triple Lie entralizers on prime rings and applications

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2024-04-18 , Revised: 2024-08-14 , Accepted: 2024-08-16 , Available online: 2025-03-24 , https://doi.org/10.7151/dmgaa.1475

Abstract:

Let R be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent P and ϕ be an additive map on R satisfying ϕ([[A, B], C]) = [[ϕ(A), B], C] = [[A, ϕ(B)], C], for any A, B, C ∈ R whenever AB = 0. In this paper, we study the structure of ϕ and prove that ϕ on R is proper, i.e. has the form ϕ(A) = λA + h(A), where λ ∈ Z(R) and h is an additive map into its center vanishing at second commutators [[A, B], C] with AB = 0. As an application of our results, we characterize generalized Lie triple derivations on R. The obtained results are applied to Banach space standard operator algebras and factor von Neumann algebras, which generalize some known results.

Keywords:

Lie triple centralizer, generalized Lie triple drivation, prime ring

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