局部环上矩阵的若干分解

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-11-03 DOI:10.1142/s0219498825500884

M. H. Bien, P. T. Nhan, N. H. T. Nhat

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引用次数: 0

摘要

设[公式:见文]是一个具有极大理想的局部环[公式:见文]，设[公式:见文]是一个大于[公式:见文]的自然数，设[公式:见文]是一个次数[公式:见文]大于[公式:见文]的一般线性群[公式:见文]中的矩阵。我们首先证明，如果矩阵[公式:见文]在[公式:见文]中为非标量，[公式:见文]在[公式:见文]中为可逆元素，则存在一个可逆元素[公式:见文]使得[公式:见文]与乘积[公式:见文]相似，其中[公式:见文]是下单三角矩阵，[公式:见文]是上三角矩阵，其对角线项为[公式:见文]。然后，我们给出了这种分解的一些应用，以找到[公式:见文本]中的矩阵分解为对易子和对合的乘积。

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Some Certain Decompositions of Matrices Over Local Rings

Let [Formula: see text] be a local ring with maximal ideal [Formula: see text], let [Formula: see text] be a natural number greater than [Formula: see text] and let [Formula: see text] be a matrix in the general linear group [Formula: see text] of degree [Formula: see text] over [Formula: see text]. We firstly show that if the matrix [Formula: see text] is nonscalar in [Formula: see text] and [Formula: see text] are invertible elements in [Formula: see text], then there exists an invertible element [Formula: see text] such that [Formula: see text] is similar to the product [Formula: see text] in which [Formula: see text] is a lower uni-triangular matrix and [Formula: see text] is an upper triangular matrix whose diagonal entries are [Formula: see text]. We then present some applications of this factorization to find decompositions of matrices in [Formula: see text] into product of commutators and involutions.

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.