Commuting Jordan Derivations on Triangular Rings Are Zero

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050353

Amin Hosseini, Wu Jing

引用次数: 0

Abstract

The main purpose of this article is to show that every commuting Jordan derivation on triangular rings (unital or not) is identically zero. Using this result, we prove that if \(\mathcal{A}\) is a \(2\)-torsion free ring that is either semiprime or satisfies Condition (P), then, under certain conditions, every commuting Jordan derivation of \(\mathcal{A}\) into itself is identically zero.

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三角形环上的换元约旦衍生为零

摘要本文的主要目的是证明三角环上的每一个换元约旦派生（无论是否为单素环）都是同零的。利用这个结果，我们证明了如果 \(\mathcal{A}\) 是一个半阶环或满足条件（P）的无簇环，那么在某些条件下，\(\mathcal{A}\) 到自身的每一个换元乔丹派生都是等零的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.