On the decompositions of infinite upper triangular matrices over rings

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.

Keywords:

• Sums of square-zero matrices
• products of unipotent matrices of index 2
• infinite matrices
• triangular matrices
• Vershik–Kerov group

AMS Subject Classifications:

• 15A23
• 15A24
• 15B33
• 20H20
• 20H25

Disclosure statement

No potential conflict of interest was reported by the authors.