The Minimum Number of Idempotent Generators of an Upper Triangular Matrix Algebra

We prove that the minimum number ν = ν( m(R)) such that them × mupper triangular matrix algebra m(R) over an arbitrary commutative ringRcan be generated as anR-algebra by ν idempotents, is given by In order to prove the result mentioned above, we show that ν(R(m)) = log2 m for everym ≥ 2, whereR(m)denotes the direct sum ofmcopies ofR. The latter result corrects an error by N. Krupnik (Comm. Algebra20, 1992, 3251–3257).