主理想整环上对称矩阵模的保逆线性映射

J4 ›› 2010, Vol. 45 ›› Issue (10): 4-8.

主理想整环上对称矩阵模的保逆线性映射

史雪莹,陈小平

南京航空航天大学金城学院数理力学系, 江苏南京 211156

收稿日期:2009-07-15 出版日期:2010-10-16 发布日期:2010-10-19
作者简介:史雪莹(1986-),女,硕士,助教,研究方向为代数学.Email:shixueying26@163.com

Linear maps preserving inverses of matrices on symmetric matrix modules over principal ideal domains

SHI Xue-ying, CHEN Xiao-ping

Department of Mathematics Physics Mechanics, Nanhang Jincheng College, Nanjing 211156, Jiangsu, China

Received:2009-07-15 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

设R是特征不为3的主理想整环,2为R中的可逆元,n和m是正整数,且n≤m。刻画了R上n阶对称矩阵模S_n(R)到R上m阶矩阵模M_m(R)上的保逆线性映射的形式。

关键词: 主理想整环;逆矩阵;线性映射

Abstract:

Let R be a principal ideal domain and the characteristic of R be not 3. Assume that 2 is a unit in R. Let n and m be positive integers with n≤m. The linear maps preserving inverses of matrices from n×n symmetric matrix modules S_n(R) onto m×m matrix modules M_m(R) over R are described.

Key words: principal ideal domain; inverse of matrix; linear map

史雪莹,陈小平. 主理想整环上对称矩阵模的保逆线性映射[J]. J4, 2010, 45(10): 4-8.

SHI Xue-ying, CHEN Xiao-ping. Linear maps preserving inverses of matrices on symmetric matrix modules over principal ideal domains[J]. J4, 2010, 45(10): 4-8.

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