三角代数上的一类非全局高阶可导非线性映射

doi:10.6040/j.issn.1671-9352.0.2020.345

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (2): 48-55.doi: 10.6040/j.issn.1671-9352.0.2020.345

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三角代数上的一类非全局高阶可导非线性映射

马帅英,张建华^*

陕西师范大学数学与信息科学学院, 陕西西安 710062

发布日期:2021-01-21
作者简介:马帅英(1997— ), 女, 硕士研究生, 研究方向为算子代数. E-mail:mashuaiying13@163.com*通信作者简介:张建华(1965— ),男, 博士, 教授, 博士生导师, 研究方向为算子代数. E-mail:jhzhang@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11471199)

A class of non-global higher derivable nonlinear maps on triangular algebras

MA Shuai-ying, ZHANG Jian-hua^*

School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China

Published:2021-01-21

摘要/Abstract

摘要： 设T =Tri(A,M,B )是三角代数,{δ_n}_n∈N:T →T 是一列映射(没有可加性的假设,其中δ₀是恒等映射)。若对任意的U,V∈T 且U与V中至少有一个是幂等元,有δ_n(UV)=∑_i+j=nδ_i(U)δ_j(V),则{δ_n}_n∈N是T上可加的高阶导子。

关键词: 三角代数, 幂等元, 高阶导子

Abstract: Let T =Tri(A,M,B )be a triangular algebra, and {δ_n}_n∈N:T →T be a family of maps(without the assumption of additivity and where δ₀ is the identity map). If {δ_n}_n∈N satisfies δ_n(UV)=∑_i+j=nδ_i(U)δ_j(V)for any U,V∈T with at least one of them is idempotent, then {δ_n}_n∈N is an additive higher derivation on T.

Key words: triangular algebra, idempotent, higher derivation

中图分类号:

O177.1

马帅英,张建华. 三角代数上的一类非全局高阶可导非线性映射[J]. 《山东大学学报(理学版)》, 2021, 56(2): 48-55.

MA Shuai-ying, ZHANG Jian-hua. A class of non-global higher derivable nonlinear maps on triangular algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 48-55.

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三角代数上的一类非全局高阶可导非线性映射

A class of non-global higher derivable nonlinear maps on triangular algebras

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