广义矩阵代数上一类非全局非线性三重高阶可导映射

doi:10.6040/j.issn.1671-9352.0.2021.247

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 97-105.doi: 10.6040/j.issn.1671-9352.0.2021.247

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广义矩阵代数上一类非全局非线性三重高阶可导映射

费秀海,张海芳^*

滇西科技师范学院数理学院, 云南临沧 677099

发布日期:2022-10-06
作者简介:费秀海(1980— ),男,博士,教授,研究方向为算子代数与算子理论.E-mail: xiuhaifei@snnu.edu.cn*通信作者简介:张海芳(1980— ),女,硕士,教授,研究方向为算子代数与算子理论.E-mail: zhanghaifang103427@yeah.net
基金资助:
国家自然科学基金资助项目(11901248);云南省教育厅基础研究基金资助项目(2022J1014);云南省2021年学术和技术后备带头人才资助项目(202105AC160089)

A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras

FEI Xiu-hai, ZHANG Hai-fang^*

School of Mathematics and Physics, West Yunnan University, Lincang 677099, Yunnan, China

Published:2022-10-06

摘要/Abstract

摘要： 设G是一个满足MN=0=NM的2-无挠的广义矩阵代数,Q={A∈G:A²=0},D={d_n}_n∈N是G上一列映射(没有可加性假设)。文章证明:若对任意n∈N,A,B,C∈G且ABC∈Q,有d_n(ABC)=∑_r+s+t=nd_r(A)d_s(B)d_t(C),则D是一个可加的高阶导子。作为应用,在三角代数上得到了相同的结论。

关键词: 广义矩阵代数, 三重高阶可导映射, 高阶导子

Abstract: Let G be a 2-torsion free generalized matrix algebra with MN=0=NM,Q={A∈G:A²=0} and D={d_n}_n∈N be a sequence mapping from G into itself(without assumption of additivity). In this paper, it is shown that if D satisfies d_n(ABC)=∑_r+s+t=nd_r(A)d_s(B)d_t(C)for all n∈N,A,B,C∈G with ABC∈Q, then D is an additive higher derivation. As its applications get that the similar conclusion on Triangular algebras.

Key words: generalized matrix algebra, triple higher derivable map, higher derivation

中图分类号:

O177.1

费秀海,张海芳. 广义矩阵代数上一类非全局非线性三重高阶可导映射[J]. 《山东大学学报(理学版)》, 2022, 57(10): 97-105.

FEI Xiu-hai, ZHANG Hai-fang. A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 97-105.

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广义矩阵代数上一类非全局非线性三重高阶可导映射

A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras

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