算子代数上(m, n)-Jordan导子的刻画

安广宇, 李建奎

数学学报 ›› 2017, Vol. 60 ›› Issue (1) : 173-184.

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PDF(481 KB)
数学学报 ›› 2017, Vol. 60 ›› Issue (1) : 173-184. DOI: 10.12386/A2017sxxb0015
论文

算子代数上(m, n)-Jordan导子的刻画

    安广宇, 李建奎
作者信息 +

Characterizations of(m, n)-Jordan Derivations on Operator Algebras

    Guang Yu AN, Jian Kui LI
Author information +
文章历史 +

摘要

R是一个环,M是一个R-双边模,mn是两个非负整数满足m+n≠0,如果δ是一个从RM的可加映射满足对任意AR,(m+nδA2)=2mAδA)+2nδAA,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n>0且mn时,每一个从RM的(m,n)-Jordan导子恒等于零.还证明了,如果AB是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n>0且mnU=[NABM]是一个|mnm-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零.

Abstract

Let R be a ring, M be an R-bimodule, m and n be two fixed nonnegative integers with m+n=0.If an additive mapping δ from R into M satisfies(m+n)δ(A2)=2mAδ(A)+2nδ(A)A for every A in R, then δ is called an(m, n)-Jordan derivation.In this paper, we prove that if R is a unital ring and M is a unital Rbimodule with a left(right) separating set generated algebraically by all idempotents in R, then every(m, n)-Jordan derivation from R into M is identical with zero whenever m, n>0 and m=n.We also show that if A and B be two unital rings, M is a faithful unital(A, B)-bimodule(N is a faithful unital(B, A)-bimodule), m, n>0 and m=n, U=[NABM] is a |mn(m-n)(m+n)|-torsion-free generalized matrix ring, then every(m, n)-Jordan derivation from U into itself is equal to zero.

关键词

(m / n)-Jordan导子 / 左(右)分离集 / 广义矩阵环

Key words

(m, n)-Jordan derivation / left(right) separating set / generalized matrix ring

引用本文

导出引用
安广宇, 李建奎. 算子代数上(m, n)-Jordan导子的刻画. 数学学报, 2017, 60(1): 173-184 https://doi.org/10.12386/A2017sxxb0015
Guang Yu AN, Jian Kui LI. Characterizations of(m, n)-Jordan Derivations on Operator Algebras. Acta Mathematica Sinica, Chinese Series, 2017, 60(1): 173-184 https://doi.org/10.12386/A2017sxxb0015

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基金

国家自然科学基金资助项目(11371136)

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