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局部环上的三阶J-拟polar矩阵

3×3 J-quasipolar Matrices over Local Rings
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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.
作者 崔建 沙玲玉 CUI Jian;SHA Lingyu(School of Mathematics and Statistics,Anhui Normal University,Wuhu Anhui 241002,China)
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)。
关键词 J-拟polar环 局部环 矩阵环 J-quasipolar ring local ring matrix ring
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