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

被引：2

作者：

Danchev, Peter V. ^{[1
]}

Dung, Truong Huu ^{[2
]}

Son, Tran Nam ^{[3
,4
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Sofia 1113, Bulgaria

[2] Dong Nai Univ, Dept Math, 9 Le Quy Don St, Bien Hoa City, Dong Nai Provin, Vietnam

[3] Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam

[4] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2024年 / 34卷 / 03期

关键词：

Traceless matrices; semi-traceless matrices; fields; division rings; images of non-commutative polynomials; POLYNOMIALS; IMAGES;

D O I：

10.1142/S0218196724500115

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：331 / 349

页数：19

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