关于中心化矩阵代数的Frobenius推广

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-07 DOI:10.1016/j.laa.2025.07.002

Qikai Wang, Haiyan Zhu

引用次数: 0

摘要

本文研究了矩阵c∈Mn(R)的中心代数Sn（c，R）是代数R的（可分）Frobenius扩展的条件。对于积分域k上的代数R，给出了当c是约当正则形式且特征值在k上时Sn(c，R)/R是（可分）Frobenius扩展的充分必要条件。我们将这一分析推广到域上的任意矩阵，并通过Frobenius扩展导出了矩阵可对角化的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Frobenius extensions about centralizer matrix algebras

This paper investigates the conditions under which the centralizer algebra

S_{n} (c, R)

of a matrix

c \in M_{n} (R)

is a (separable) Frobenius extension of the algebra R. For an algebra R over an integral domain

k

, we provide necessary and sufficient conditions for

S_{n} (c, R) / R

to be a (separable) Frobenius extension when c is in Jordan canonical form with eigenvalues in

k

. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.