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.
Disclosure statement
No potential conflict of interest was reported by the authors.