[1]刘 丹,张建华,宋明亮.三角代数上Jordan同构的刻画[J].南京师大学报(自然科学版),2023,46(04):1-4.[doi:10.3969/j.issn.1001-4616.2023.04.001]
　Liu Dan,Zhang Jianhua,Song Mingliang.Characterizations of Jordan Isomorphisms of Triangular Algebras[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(04):1-4.[doi:10.3969/j.issn.1001-4616.2023.04.001]
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三角代数上Jordan同构的刻画()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年04期
页码:
1-4
栏目:
数学
出版日期:
2023-12-15

文章信息/Info

Title:
Characterizations of Jordan Isomorphisms of Triangular Algebras
文章编号:
1001-4616(2023)04-0001-04
作者:
刘 丹1; 张建华2; 宋明亮1
(1.江苏第二师范学院数学科学学院,江苏 南京 210013)
(2.陕西师范大学数学与统计学院,陕西 西安 710062)
Author(s):
Liu Dan1; Zhang Jianhua2; Song Mingliang1
(1.School of Mathematical Sciences,Jiangsu Second Normal University,Nanjing 210013,China)
(2.School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710062,China)
关键词:
三角代数; Jordan同构; 零积
Keywords:
triangular algebra;  Jordan isomorphism;  zero product
分类号:
O177.1
DOI:
10.3969/j.issn.1001-4616.2023.04.001
文献标志码:
A
摘要:
设U=Tri(A,M,B)是三角代数,V是2-无挠含单位的代数. 本文证明了线性双射φ:U→V是Jordan同构的充要条件是φ保单位且下列条件之一成立:(1)φ(x。y)=φ(x)。φ(y),其中x,y∈U满足xy=0.(2)φ(x。y)=φ(x)。φ(y),其中x,y∈U满足x。y=0.(3)φ(x。y)=φ(x)。φ(y),其中x,y∈U满足xy=yx=0.
Abstract:
Let U=Tri(A,M,B)be a triangular algebra and let V be a unitial 2-torsion free algebra. It is shown that a linear bijection φ:U→V is Jordan isomorphism if and only if φ is unital and one of the following statements holds:(1)φ(x。y)=φ(x)。φ(y)for x,y∈U with xy=0;(2)φ(x。y)=φ(x)。φ(y)for x,y∈U with x。y=0;(3)φ(x。y)=φ(x)。φ(y)for x,y∈U with xy=yx=0.

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备注/Memo

备注/Memo:
收稿日期:2022-02-18.
基金项目:国家自然科学基金项目(11901248).
通讯作者:刘丹,博士,讲师,研究方向:算子代数与算子理论. E-mail:ldyfusheng@126.com
更新日期/Last Update: 2023-12-15