保持交换环上两类矩阵运算的映射  

Maps of Preserving Two Kinds of Matrix Operations on Commutative Rings

作　　者：王雨轩 霍东华 WANG Yuxuan;HUO Donghua(School of Mathematical Science, Mudanjiang Normal University, Mudanjiang 157012, China)

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157012

出　　处：《高等数学研究》2022年第1期49-53,56,共6页Studies in College Mathematics

基　　金：黑龙江省省属高等学校基本科研业务费校级科研团队建设专项项目(1355TD005);牡丹江师范学院国家级课题培育项目(GP2020005).

摘　　要：主要针对交换环上两类矩阵的保持问题进行展开:(1)刻画了交换环上全矩阵空间和上三角形矩阵空间的保持反对合矩阵映射的形式.(2)研究了交换环上n阶上三角形矩阵空间的保持伴随矩阵映射的形式.We focus on the problem of preserving two kinds of matrices over commutative rings:(1)characterize the forms of preserving anti-involution matrix mapping in the space of full matrices and upper triangular matrices over commutative ring;(2)study the form of preserving adjoint matrix mapping of triangular matrix space of n order over commutative ring.

关 键 词：全矩阵 上三角矩阵 反对合矩阵 伴随矩阵 保持问题 

分 类 号：O151.2[理学—数学]