保持{1,2,T}-逆的加法映射

数学季刊 ›› 2009, Vol. 24 ›› Issue (4): 590-597.

保持{1,2,T}-逆的加法映射

1. Department of Foundation Courses, Huai'an College of Information Technology2. College of Science, Nanjing University of Aeronautics and Astronautics3. Faculty of Mathematics and Physics, Huaiyin Institute of Technology

收稿日期:2006-06-06 出版日期:2009-12-30 发布日期:2023-06-19
作者简介:RONG Jian-ying(1978-), female, native of Heze, Shandong, a lecturer of Huai'an College of Information Technology, M.S.D., engages in linear algebra.
基金资助:
Supported by the NNSF of China(10371054)；

Additive Maps Preserving {1, 2, T}-inverses

1. Department of Foundation Courses, Huai'an College of Information Technology2. College of Science, Nanjing University of Aeronautics and Astronautics3. Faculty of Mathematics and Physics, Huaiyin Institute of Technology

Received:2006-06-06 Online:2009-12-30 Published:2023-06-19
About author:RONG Jian-ying(1978-), female, native of Heze, Shandong, a lecturer of Huai'an College of Information Technology, M.S.D., engages in linear algebra.
Supported by:
Supported by the NNSF of China(10371054)；

摘要/Abstract

摘要： Let F be a field of characteristic not 2 and 3.Let f: M_mn(F)→M_mn(F) be an additive map preserving {1,2,T}-inverse, i.e. f(A)=f(A)f(B)^Tf(A), f(B)= f(B)f(A)^Tf(B) for any A,B∈M_mn(F) with A=AB^TA, B=BA^TB. In this paper, we give the sufficient and necessary condition for f to be such a map.

关键词: additive map, preserving {1, 2, T}-inverse

Abstract: Let F be a field of characteristic not 2 and 3.Let f: M_mn(F)→M_mn(F) be an additive map preserving {1,2,T}-inverse, i.e. f(A)=f(A)f(B)^Tf(A), f(B)= f(B)f(A)^Tf(B) for any A,B∈M_mn(F) with A=AB^TA, B=BA^TB. In this paper, we give the sufficient and necessary condition for f to be such a map.

Key words: additive map, preserving {1, 2, T}-inverse

中图分类号:

O151.21

荣建英, 岳勤, 刘绪庆. 保持{1,2,T}-逆的加法映射[J]. 数学季刊, 2009, 24(4): 590-597.

RONC Jian-ying, YUE Qin, LIU Xu-qing. Additive Maps Preserving {1, 2, T}-inverses[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(4): 590-597.