局部环上的三阶J-拟polar矩阵  

3×3 J-quasipolar Matrices over Local Rings

作　　者：崔建 沙玲玉 CUI Jian;SHA Lingyu(School of Mathematics and Statistics,Anhui Normal University,Wuhu Anhui 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《大学数学》2023年第2期8-14,共7页College Mathematics

基　　金：安徽省高等学校省级质量工程项目(2021jyxm0517;2021xxkc058)。

摘　　要：基于群自同构及矩阵的相关性质,研究了三阶矩阵环的两类特殊子环L(R)与S(R)的J-拟polar性,给出了在局部环条件下上述两类矩阵环为J-拟polar环的充分必要条件,证明了若R是局部环,则L(R)是J-拟polar环当且仅当S(R)是J-拟polar环当且仅当R是UB-环且R/J(R)■2.Based on automorphisms of groups and some properties of matrices,we investigate the J-quasipolarity of L(R)and S(R),two classes of special subrings of the 3×3 matrix ring.Under the condition of local rings,the necessary and sufficient conditions for L(R)and S(R)to be J-quasipolar are studied.We prove that if R is a local ring,then L(R)is J-quasipolar if and only if S(R)is J-quasipolar if and only if R is a UB-ring and R/J(R)■2.

关 键 词：J-拟polar环 局部环 矩阵环 

分 类 号：O153.3[理学—数学]