On the decompositions of infinite upper triangular matrices over rings. Issue 9 (2nd September 2018)

• Record Type: Journal Article
• Authors: Hou, Xin; Li, Shangzhi; Zheng, Qingqing
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 9(2018)
• Page Start: 1917
• Page End: 1924
• Publication Date: 2018-09-02
• Subjects: Sums of square-zero matrices -- products of unipotent matrices of index 2 -- infinite matrices -- triangular matrices -- Vershik–Kerov group; 15A23 -- 15A24 -- 15B33 -- 20H20 -- 20H25; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1376615
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: Let R be an arbitrary associative ring with identity 1. We prove that any infinite strictly upper triangular matrix (indexed by ) over R can be decomposed into a sum of at most four square-zero matrices, and any infinite upper unitriangular matrix (indexed by ) over R can be decomposed into a product of at most four unipotent matrices of index 2.