The minimum number of idempotent generators of an upper triangular matrix algebra (Q1270387)

The authors prove the main result of the paper: The minimum number \(\nu=\nu(U_m(R))\) such that the \(m\times m\) upper triangular matrix algebra \(U_m(R)\) over an arbitrary commutative ring \(R\) can be generated as an \(R\)-algebra by \(\nu\) idempotents, is given by \[ \nu(U_m(R))=\begin{cases}[\log_2m]+1,\quad &\text{if }m=2,3,4;\\ [\log_2m],\quad &\text{if }m\geq 5.\end{cases} \] Examples are also given. The authors search for a new internal characterization of upper triangular matrix rings, and of structural matrix rings in general which is their long term goal, is the origin of this paper.