形式三角矩阵半环的自同构与反自同构  

Automorphisms and Opposite Automorphisms of Formal Triangular Matrix Semi-rings

作　　者：张源野 谭宜家[1] ZHANG Yuanye;TAN Yijia(College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福州大学数学与计算机科学学院,福州350108

出　　处：《西南大学学报（自然科学版）》2021年第12期67-73,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11971111);福建省自然科学基金面上项目(2016J01012).

摘　　要：研究了形式三角矩阵半环Tri(R,M,S)的自同构和反自同构.证明了:半环Tri(R,M,S)的任一自同构可由半环R,S的自同构和(R,S)-双半模M的一个半线性自同构来表示;半环Tri(R,M,S)的任一反自同构可由半环R到S的一个反同构、S到R的一个反同构和(R,S)-双半模M的一个半线性反自同构来表示.The automorphisms and the opposite automorphisms of a formal triangular matrix semi-ring Tri(R,M,S)are studied in this paper.It is proved that any automorphism of the semi-ring Tri(R,M,S)can be expressed by an automorphism of the semi-ring R and an automorphism of the semi-ring S and a half-linear automorphism of the(R,S)-bi-semimodule M and that any opposite automorphism of Tri(R,M,S)can be expressed by an opposite isomorphism of R onto S and an opposite isomorphism of S onto R and a half-linear opposite automorphism of the(R,S)-bi-semimodule M.

关 键 词：自同构 反自同构 半环 形式三角矩阵半环 半模 

分 类 号：O151.21[理学—数学]