The Minimum Number of Idempotent Generators of a Complete Blocked Triangular Matrix Algebra

Let R be a complete blocked triangular matrix algebra over an infinite field F. Assume that R is not an upper triangular matrix algebra or a full matrix algebra. We prove that the minimum number ν = ν(R) such that R can be generated as an F-algebra by ν idempotents, is given by[formula]where m1 is the number of 1 × 1 diagonal blocks of R. We also show that R can be generated as an F-algebra by two elements, and if m1 = 0, R can be generated by an idempotent and a nilpotent element.