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.
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 bijectionφ:U→V is Jordan isomorphism if and only ifφis 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.
作者
刘丹
张建华
宋明亮
Liu Dan;Zhang Jianhua;Song Mingliang(School of Mathematical Sciences,Jiangsu Second Normal University,Nanjing 210013,China;School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710062,China)
出处
《南京师大学报（自然科学版）》
CAS
北大核心
2023年第4期1-4,共4页
Journal of Nanjing Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11901248).
关键词
三角代数
JORDAN
同构
零积
triangular algebra
Jordan isomorphism
zero product
