| 徐华博,王利萍.环自同构诱导的广义循环矩阵[J].数学年刊A辑,2024,45(4):423~436 |
| 环自同构诱导的广义循环矩阵 |
| Generalized Circulant Matrices Related to Automorphisms |
| Received:October 07, 2023 Revised:August 26, 2024 |
| DOI：10.16205/j.cnki.cama.2024.0029 |
| 中文关键词: 广义循环矩阵 Hopf代数 不动点子环 |
| 英文关键词:Generalized circulant matrix, Hopf algebra, Invariant subring |
| 基金项目:北京市青年拔尖人才项目(No.21351918007)； 北京建筑大学研究能力提升计划(No.X22026) |
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| 中文摘要: |
| 设φ是结合环R上阶为n的自同构映射.根据自同构φ,作者引入广义循环矩阵的概念.令Rφ是R关于φ的不动点子环,C_n（φ,R）为R上所有n×n广义循环矩阵构成的集合.作者证明了C_n（φ,R）是自同态环EndRφ（R~n）的子环.此外,还证明了如果R是Rφ上交换的Hopf代数,则C_n（φ,R）也是Rφ上的Hopf代数. |
| 英文摘要: |
| The authors introduce the definition of generalized circulant matrices which is the
generalization of circulant matrices. Let R be an associative ring with an automorphism ? of
order n. They consider the set Cn(?, R) of all the generalized circulant n×n matrices over R
for any positive integer n. It is shown that Cn(?, R) is a subring of the endomorphism ring
of the R? -module Rn, where R? is the invariant subring of R with respect to ?. Moreover,
if R is a commutative Hopf algebra over R?, then Cn(?, R) is also a Hopf algebra over R?. |
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