分割环上无踪和半无踪矩阵的乘积及其应用

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2024-03-26 DOI:10.1142/s0218196724500115

Peter V. Danchev, Truong Huu Dung, Tran Nam Son

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引用次数: 0

摘要

在本文中，我们证明了划分环上的每个矩阵都可以表示为最多 10 个无踪矩阵的乘积，以及最多 4 个半无踪矩阵的乘积。通过应用这一结果和迄今为止获得的其他结果，我们证明了某些代数的元素具有一些相当有趣的非难分解，即分解为非交换多项式的图像的乘积。

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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Products of traceless and semi-traceless matrices over division rings and their applications

In this paper, we prove that every matrix over a division ring is representable as a product of at most 10 traceless matrices as well as a product of at most four semi-traceless matrices. By applying this result and the obtained so far other results, we show that elements of some algebras possess some rather interesting and nontrivial decompositions into products of images of non-commutative polynomials.

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.