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

@article{Merwe1999TheMN,
  title={The Minimum Number of Idempotent Generators of a Complete Blocked Triangular Matrix Algebra},
  author={A. B. van der Merwe and Leon van Wyk},
  journal={Journal of Algebra},
  year={1999},
  volume={222},
  pages={190-203}
}
Abstract 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. 
Algebras Generated by Two Quadratic Elements
Let K be a field of any characteristic and let R be an algebra generated by two elements satisfying quadratic equations. Then R is a homomorphic image of F = K ⟨x, y | x 2 + ax + b = 0, y 2 + cy + d

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