The minimum number of idempotent generators of an upper triangular matrix algebra

We prove that the minimum number v = v(Script U signm(R)) such that the m × m upper triangular matrix algebra Script U signm(R) over an arbitrary commutative ring R can be generated as an R-algebra by v idempotents, is given by (formula presented) In order to prove the result mentioned above, we show that v(R(m)) = ⌈log2 m⌉ for every m ≥ 2, where R(m) denotes the direct sum of m copies of R. The latter result corrects an error by N. Krupnik (Comm. Algebra 20, 1992, 3251-3257). © 1998 Academic Press.