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Characterizations of Jordan Isomorphisms of Triangular Algebras(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2023年04期
Page:
1-4
Research Field:
数学
Publishing date:

Info

Title:
Characterizations of Jordan Isomorphisms of Triangular Algebras
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)
Keywords:
triangular algebra;  Jordan isomorphism;  zero product
PACS:
O177.1
DOI:
10.3969/j.issn.1001-4616.2023.04.001
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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Last Update: 2023-12-15