期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
一类交换环上全矩阵半群的自同构
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1. 江西理工大学 理学院, 江西 赣州 341000;
2. 徐州工程学院 数学与物理科学学院, 江苏 徐州 221008 -
DOI：10.13763/j.cnki.jhebnu.nse.2015.02.001
Automorphisms of the Full Matrix Semigroup over a Class of Commutative Rings
摘要/Abstract
摘要：
设R是有1的连通交换环,Mn(R)是R上所有n×n矩阵组成的矩阵乘法半群,ø是Mn(R)上的任一半群自同构.证明了若R上的幂等矩阵均可相似对角化,则存在可逆矩阵 P ∈Mn(R),环R的自同构θ,使得ø(A)= PAθP-1,∀ A ∈Mn(R).
Abstract：
Let R be a connected commutative ring with 1,Mn(R) the multiplicative semigroup consisting of all n×n matrices over R, ø an arbitrary automorphism of Mn(R).In this paper,we prove that if every idempotent matrix over R is similar to a diagonal matrix,then there exist an invertible matrix P ∈Mn(R) and an automorphism θ of R,such that ø(A)= PAθP-1,∀A ∈Mn(R).
关键词
Key words：
automorphism
;
matrix semigroup
;
semigroup
;
connected ring
参考文献 6
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