一类环上的Jordan可导映射

J4 ›› 2012, Vol. 47 ›› Issue (4): 5-10.

一类环上的Jordan可导映射

曹宗霞，张建华

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2011-10-07 出版日期:2012-04-20 发布日期:2012-06-28
作者简介:曹宗霞(1985- ),女,硕士研究生,研究方向为算子代数. Email:caozongxia@126.com
基金资助:
国家自然科学基金资助项目(10726043)

Additive Jordan derivable maps of certain rings

CAO Zong-xia, ZHANG Jian-hua

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi， China

Received:2011-10-07 Online:2012-04-20 Published:2012-06-28

摘要/Abstract

摘要：

证明了一类环R上的可加映射δ满足对任意的S,T∈R且ST=P均成立δ(S。T)=δ(S)。T+S。δ(T)当且仅当δ是一个Jordan导子,其中ST=ST+TS为Jordan积,P为环R中的一个非平凡幂等元。

关键词: 环;Jordan导子; Jordan可导映射

Abstract:

Under some mild conditions on a unital ring R, we show that every additive map δ from R into itself satisfies δ(S。T)=δ(S)。T+S。δ(T) for any S,T∈R with ST=P if and only if δ is a Jordan derivation, where S。T=ST+TS is the Jordan product and P is a nontrivial idempotent of ring R.

Key words: ring; Jordan derivation; Jordan derivable map

曹宗霞，张建华. 一类环上的Jordan可导映射[J]. J4, 2012, 47(4): 5-10.

CAO Zong-xia, ZHANG Jian-hua. Additive Jordan derivable maps of certain rings[J]. J4, 2012, 47(4): 5-10.

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